Geometry, Analysis & Gravitation
This is the group research seminar for Geometry, Analysis and Gravitation.
Time: Tuesday at 2pm
Location: MB 503 Mathematics Seminar Room
Organisers: Huy Nguyen and Katy Clough. Please email us in case you have any questions or want to give a talk yourself.

DateRoomSpeakerTitle

03/10/2023 2:00 PMMB503 Mathematics Seminar RoomMarco Meineri (Turin)Renormalization group flows in AdS and the bootstrap program
We consider the renormalization group flow of a quantum field theory (QFT) in Antide Sitter (AdS) space. We derive sum rules that express UV data and the energy of a chosen eigenstate in terms of the spectral densities and certain correlation functions of the theory. In two dimensions, this leads to a bootstrap setup that involves the UV central charge and may allow us to follow a Renormalization Group (RG) flow nonperturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition, which applies to threepoint functions involving one bulk and two boundary operators.

26/09/2023 2:00 PMMB503 Mathematics Seminar RoomLuke Peachy (WarwickTwo dimensional expanding Ricci solitons
Expanding Ricci solitons are central to our understanding of both the longtime behaviour of Ricci flow, and the shorttime asymptotics of Ricci flow as it desingularises rough initial data. By utilising a onetoone correspondence between complete Ricci flows and their weak initial data, we complete the classification of expanding Ricci solitons in two dimensions. This is joint work with Peter Topping. 
11/12/2023 2:00 PMMB503 Mathematics Seminar RoomSimon Guisset (QMUL)TBA

28/11/2023 2:00 PMMB503 Mathematics Seminar RoomTBATBA

14/11/2023 2:00 PMMB503 Mathematics Seminar RoomTBATBA

05/12/2023 2:00 PMMB503 Mathematics Seminar RoomHong Qi (QMUL)TBA

21/11/2023 2:00 PMMB503 Mathematics Seminar RoomMax Stolarski (Warwick)TBA

31/10/2023 2:00 PMMB503 Mathematics Seminar RoomEdgar Gasperin (Lisbon)TBA

24/10/2023 2:00 PMMB503 Mathematics Seminar RoomRodolfo Russo and Carlo Heissenberg QMULTBA

10/10/2023 2:00 PMMB503 Mathematics Seminar RoomMasanori Hanada QMULTBA

17/10/2023 2:00 PMMB503 Mathematics Seminar RoomAndrea Mondino (Oxford)TBA

11/05/2023 2:00 PMMB503 Mathematics Seminar Room (NOTE: DIFFERENT DAY!)Chris StevensThe conformal field equations, black holes, gravitational waves and the NewmanPenrose constantsIn recent years, a (numerically) wellposed Initial Boundary Value Problem (IBVP) for the generalized conformal field equations has been put forward. These equations regularly extend the Einstein equations to include "infinity" and the associated IBVP has been used to successfully evolve, in the fully nonlinear regime, a black hole spacetime perturbed with a gravitational wave. This framework allows for direct calculations of global quantities defined at infinity, such as the BondiSachs energymomentum, and we have used it to successfully reproduce the BondiSachs mass loss.In this talk, two applications will be discussed:Linear perturbations of black holes are well known and the associated oscillations in the Weyl curvature are known as quasinormal modes. In recent work, we investigated the analogous nonlinear curvature oscillations and how they decay to the linear regime. In doing so, we have observed that only a short amount of physical proper time can be resolved numerically in the conformal representation. Ideas to alleviate this problem will be put forward.
Another recent application was the calculation of the NewmanPenrose Constants (NPC). These are five complex quantities defined on null infinity that are absolutely conserved if it is smooth. In stationary spacetimes, they can be written terms of mass and angular momentum moments, but their physical interpretation in nonstationary spacetimes is still lacking. We compute, for the first time, the NPC in a general setting and show that they remain constant, implying smoothness of null infinity to at least the level of our numerical precision.

18/04/2023 2:00 PMMB503 Mathematics Seminar RoomMatteo Capoferri (HeriotWatt University)Beyond the Hodge Theorem: curl and asymmetric pseudodifferential projections
Abstract: Consider a single photon living in curved space. It is described by Maxwell’s equations. We seek solutions harmonic in time. This reduces to the spectral problem for the operator curl, whose spectrum is, in general, asymmetric about zero (think particle/antiparticle).
Spectral asymmetry is a classical subject in analysis and geometry, whose ori gins lie in the papers of Atiyah, Patodi and Singer. In this talk I will discuss a new approach to the study of spectral asymmetry based on the use of pseu dodifferential techniques developed in a series of recent joint papers by Dmitri Vassiliev and myself. 
05/04/2023 2:00 PMMB502 (Committee Room) (NOTE : DIFFERENT DAY AND ROOM!)Miguel BezaresKdynamics: Gravitational wave generation in Dark energy
We will discuss recent efforts to understand gravitational wave generation in Dark energy models. I will consider a class of alternative theories of gravity known as kessence. This theory is a cosmologically relevant scalartensor theory that involves firstorder derivative selfinteractions, which pass all existing gravitational wave bounds and provides a screening mechanism. In this talk, I will present our numerical simulations of this theory considering three scenarios: nonlinear stellar oscillations, gravitational collapse and binary neutron stars.

21/03/2023 3:00 PMMB503 Mathematics Seminar RoomBarry Wardell (University College Dublin)Gravitational waveforms for compact binaries from secondorder selfforce theory
Abstract:
Extreme mass ratio inspirals (EMRIs) are expected to be a key source of gravitational waves for the LISA mission. In order to extract the maximum amount of information from EMRI observations by LISA, it is important to have an accurate prediction of the expected waveforms. In particular, it will be necessary to have waveforms that incorporate effects that appear at second order in the mass ratio. In this talk I will present the latest progress towards this goal, including recent results for the secondorder gravitationalwave energy flux and for the gravitational waveform. 
28/02/2023 2:00 PMMB503 Mathematics Seminar RoomMegan GriffinPickeringRecent results on the quasineutral limit for the ionic VlasovPoisson system
VlasovPoisson type systems are well known as kinetic models for plasma. The precise structure of the model differs according to which species of particle it describes, with the `classical’ version of the system describing the electrons in a plasma. The model for ions, however, includes an additional exponential nonlinearity in the equation for the electrostatic potential, which creates several mathematical difficulties. For this reason, the theory of the ionic system has so far not been as fully explored as the theory for the electron equation.
A plasma has a characteristic scale, the Debye length, which describes the scale of electrostatic interaction within the plasma. In real plasmas this length is typically very small, and in physics applications frequently assumed to be very close to zero. This motivates the study of the limiting behaviour of VlasovPoisson type systems as the Debye length tends to zero relative to the observation scale—known as the ‘quasineutral’ limit. In the case of the ionic model, the formal limit is the kinetic isothermal Euler system; however, this limit is highly nontrivial to justify rigorously and known to be false in general without very strong regularity conditions and/or structural conditions.
I will present a recent work, carried out in collaboration with Mikaela Iacobelli, in which we prove the quasineutral limit for the ionic VlasovPoisson system for a class of rough (L^\infty) data: that is, data that may be expressed as perturbations of an analytic function, small in the sense of MongeKantorovich distances. The smallness of the perturbation that we require is much less restrictive than in the previously known results. 
21/02/2023 2:00 PMMB503 Mathematics Seminar RoomAlex Mramor (Copenhagen)The mean curvature flow, singularities, and entropy
Abstract: The mean curvature flow is an example of a geometric flow, where in this case one deforms a submanifold according to its mean curvature vector. Like many such flows though the mean curvature flow will develop singularities, where the flow “pinches.” The entropy, in the sense of Colding and Minicozzi, is an interesting arealike monotone quantity under the flow, for one because it can constrain what sorts of singularity models may arise, and has played an important role in many recent developments. In this talk, after introducing the relevant notions we’ll discuss some of these results, including some joint work with S. Wang.

14/02/2023 2:00 PMMB503 Mathematics Seminar RoomRoberto OliveriTidal deformations on binary systems induced by an external Kerr black hole
Abstract:
The dynamics of a binary system moving in the background of a black hole is affected by tidal forces. In this talk, we derive the electric and magnetic tidal moments at quadrupole order induced by a Kerr black hole. We make use of these moments in the scenario of a hierarchical triple system made of a Kerr black hole and an extrememass ratio binary system consisting of a Schwarzschild black hole and a test particle. We study how the secular dynamics of the test particle in the binary system is distorted by the presence of tidal forces from a much larger Kerr black hole. We compute the shifts in the physical quantities for the secular dynamics of the test particle and show that they are gaugeinvariant. In particular, we apply our formalism to the innermost stable circular orbit for the test particle and to the case of the photon sphere. 
31/01/2023 2:00 PMMB503 Mathematics Seminar Room (Zoom)Elena Giorgi (Columbia)Black Hole Stability Problems in GR
Abstract: In this talk, I will give an overview of the stability problems for black hole solutions, starting with the mode stability results in black hole perturbation theory in the 80’s to more recent mathematical proofs, as the linear and the fully nonlinear stability of black hole solutions require new mathematical techniques. Finally, I will present some aspects of our recent proof with Klainerman and Szeftel of the nonlinear stability of the slowly rotating Kerr black hole.

07/03/2023 2:00 PMMB503 Mathematics Seminar Room (Zoom)Edgar Gasperin (Lisbon)The goodbadugly system near spatial infinity on flat spacetime
Abstract: A system of equations that serves as a model for the Einstein field equation in generalised harmonic gauge called the goodbadugly system is studied in the region close to null and spatial infinity in Minkowski spacetime. This analysis is performed using H. Friedrich's cylinder construction at spatial infinity and defining suitable conformally rescaled fields. The results are translated to the physical set up to investigate the relation between the polyhomogeneous expansions arising from the analysis of linear fields using the i0cylinder framework and those obtained through a heuristic method based on Hörmander's asymptotic system.

24/01/2023 2:00 PMMB503 Mathematics Seminar RoomTarek Anous (QMUL)Matrix models and the emergence of 2d gravity
Abstract: In this seminar I will review how the quantum path integral of 2 dimensional JackiwTeitelboim (JT) gravity (with arbitrary numbers of boundaries) is computed by a particular Hermitian matrix integral. This duality is perturbative, meaning the equivalence is demonstrated by matching the perturbation series order by order in both descriptions. Building on this, I will describe an altogether different class of matrix integrals, namely one involving unitary matrices, which is also dual to JT gravity when parameters are tuned in a particular way. This allows a nonperturbative view of the JT theory as a particular phase of a more general theory, tying into the structure of phase transitions more familiar in statistical physics.

14/03/2023 2:00 PMMB503 Mathematics Seminar RoomMichele Coti Zelati (Imperial)Timescales in fluid mechanics
Abstract:
We present recent results on timescales separation in fluid
mechanics. The fundamental mechanism to detect in a precise
quantitative manner is commonly referred to as fluid mixing. Its
interaction with advection, diffusion and nonlocal effects produces a
variety of timescales which explain many experimental and numerical
results related to hydrodynamic stability and turbulence theory. 
07/02/2023 2:00 PMMB503 Mathematics Seminar RoomJean Lagacé (KCL)Conformal maps in spectral geometry
In this talk, I will explain how uniformisation and conformal maps have been used and keep being used nowadays to obtain results in the spectral geometry of surfaces. Whether it is for shape optimisation or eigenvalue asymptotics, much can be said from the careful analysis of conformal factors. Along the way, this will also be a good opportunity to survey the field of twodimensional spectral geometry.

13/12/2022 2:00 PMMB503 Mathematics Seminar RoomBolys Sabitbek (QMUL)Potential wells and applications to semilinear wave equations
Abstract: In this talk, I will present the family of potential wells to the initial boundary problem of semilinear wave equations. This gives the vacuum isolating solutions and threshold result of global existence and nonexistence of solutions.

22/11/2022 2:00 PMMB503Daniela Doneva (Tübingen)Astrophysical manifestations of spontaneous scalarization
Spontaneous scalarization is among the most interesting mechanisms to
endow compact objects with scalar hair while leaving the weak field
regime of gravity unaltered with respect to GR. In the present talk we
will discuss the dynamics of spontaneous scalarization of black holes
and neutron stars in extended scalartensor theories of gravity,
focusing primarily on some of the most interesting cases from an
astrophysical point of view. These include binary merger, stellar core
collapse, and gravitational phase transitions. The electromagnetic and
gravitational wave signatures, as well as the prospect for their
detectability, will be also discussed. 
25/10/2022 2:00 PMMB503 Mathematics Seminar RoomUli Sperhake (Cambridge)Longlived inverse chirp gravitational waves in scalartensor gravity
Abstract: In this talk, we model the gravitational collapse of stars in
massive scalartensor gravity. In this theory, the two tensorial
gravitationalwave polarization modes are complemented by a massive
breathing mode. This latter mode is triggered by the spontaneous
scalarization mechanism discovered by Damour and EspositoFarese; its
radiation exhibits a drastically different behaviour dominated by the
dispersive character of the mass term which leads to quasimonochromatic
signals that can last years or even centuries. This smokinggun effect
offers unique opportunities to test this class of theories. We also
briefly discuss the overlap of numerous such signals arising from multiple
supernova events in the local universe and compare the resulting
gravitationalwave energy density with present constraints from LIGOVirgo
observations. 
18/10/2022 3:30 PMTBAEwelina Zatorska (Imperial)The dissipative AwRascle system: existence theory and hardcongestion limit.
Abstract: In this talk I am going to analyse the compressible dissipative hydrodynamic model of crowd motion or of granular flow. The model resembles the famous AwRascle model of traffic, except that the difference between the actual and the desired velocities (the offset function) is a gradient of the density function, and not a scalar. This modification gives rise to a dissipation term in the momentum equation that vanishes when the density is equal to zero.
I will compare the dissipative AwRascle system with the compressible Euler and compressible NavierStokes equations, and back it up with two existence and illposedness results. In the last part of my talk I will explain the proof of conjecture made by LefebvreLepot and Maury, that the hard congestion limit of this system (with singular offset function) leads to congested compressible/incompressible Euler equations. 
15/11/2022 2:00 PMMB503 Mathematics Seminar RoomProf Nils Andersson (University of Southampton)Nonequilibrium aspects of neutron star mergers
Deviations from beta equilibrium impact on the fineprint details of the gravitationalwave signal from neutronstar binary inspiral and merger. During the inspiral phase, the individual neutron stars are cold enough that the Urca reactions cannot establish equilibrium on the inspiral timescale. This leads to the presence of composition gmodes which may become resonant as the system evolves through the sensitivity band of groundbased detectors. In contrast, during the hot postmerger phase the reactions are expected to be fast enough that they need to be accounted for (at least in parts of parameter space). In this talk I will tie together the two phases of the binary problem, outlining the role of composition effects during the inspiral as well as the emergence of an effective bulk viscosity after merger. Framing the discussion in the context of stateoftheart merger simulations, I will suggest that the nonequilibrium physics impact on the gravitationalwave signal at the “few percent level”, likely undetectable with the LIGO instruments but plausibly within reach of third generation detectors like the Einstein Telescope and the Cosmic Explorer.

01/11/2022 2:00 PMMB503 Mathematics Seminar RoomIlia Musco (La Sapienza)Formation of primordial black holes during the QCD phase transition
ABSTRACT: The formation of Primordial black holes is naturally enhanced during the quarkhadron phase transition, because of the softening of the equation of state occurring during this epoch: at a scale between 1 and 3 solar masses, the threshold is reduced of about 10% with a corresponding abundance of primordial black holes significantly increased by more than 100 times. We show that a subpopulation of primordial black black holes formed during the QCD epoch, in the solar mass range, is compatible with the current observational constraints, and could explain some of the interesting sources emitting gravitational waves detected by LIGO/VIRGO in the black hole mass gap, such as GW190814, and other light events

04/10/2022 2:00 PMMB503 Mathematics Seminar RoomMatthew Elley (KCL)Dynamical scalarization and descalarization in binary black hole mergers in EinsteinscalarGaussBonnet gravity
It has been shown that, for certain modified theories in which a scalar field is coupled with the GaussBonnet curvature invariant, black hole spacetimes can undergo a tachyonic instability which culminates in a nontrivial stationary scalar configuration. This mechanism is known as spontaneous scalarization, and its onset is controlled by parameters such as the coupling strength, mass and spin of the black hole. Thus, dynamical binary systems allow for a variety of configurations that depend on these parameters. For example, two scalarized black holes can merge to form a larger remnant that has no scalar profile due to the weaker spacetime curvature near the horizon, a mechanism known as dynamical descalarization. In this talk, I will be discussing my work on modelling binary black hole systems in scalarGaussBonnet gravity to identify the possible configurations. Knowledge of these configurations can assist in the identification of the gravitational waveform modifications due to the scalar field and can provide estimates of the constraints on the theory.

27/09/2022 2:00 PMMB503 Mathematics Seminar RoomShengwen Wang (QMUL)A Brakke type regularity theorem for the AllenCahn flow
Abstract: We will talk about an analogue of the Brakke's local regularity theorem for the $\epsilon$ parabolic AllenCahn equation. In particular, we show uniform $C_{2,\alpha}$ regularity for the transition layers converging to smooth mean curvature flows as $\epsilon$ tend to 0 under the almost unitdensity assumption. This can be viewed as a diffused version of the Brakke regularity for the limit mean curvature flow. This talk is based on joint work with Huy Nguyen.

11/10/2022 2:00 PMMB503 Mathematics Seminar RoomAli Seraj (QMUL)Gravitational memory effects; from theory to observation
Abstract: In this talk, I will give an overview on "gravitational memory effects”. I will address the following questions: what are they? How can they be observed? and what are their implications for fundamental physics? I will emphasise my contribution in this field.

29/03/2022 2:00 PMMB503  Maths Seminar RoomPatricia SchmidtPutting spin into black hole binaries
abstract: I will present the derivation of the antipodal matching relations used to demonstrate the equivalence between soft graviton theorems and BMS charge conservation across spatial infinity. To this end I will provide a precise map between Bondi data at null infinity and BeigSchmidt data at spatial infinity in a context appropriate to the gravitational scattering problem and celestial holography. I will also demonstrate that, among various proposals of BMS charges at null infinity found in the literature, only a subset match the conserved charges at spatial infinity and are therefore preferred from that perspective.
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05/04/2022 2:00 PMMB503  Maths Seminar RoomKevin NguyenCharge and antipodal matching across spatial infinityAbstract: I will present the derivation of the antipodal matching relations used to demonstrate the equivalence between soft graviton theorems and BMS charge conservation across spatial infinity. To this end I will provide a precise map between Bondi data at null infinity and BeigSchmidt data at spatial infinity in a context appropriate to the gravitational scattering problem and celestial holography. I will also demonstrate that, among various proposals of BMS charges at null infinity found in the literature, only a subset match the conserved charges at spatial infinity and are therefore preferred from that perspective.

22/03/2022 2:00 PMMB503  Maths Seminar RoomSean HartnollThe classical interior of black holes in holographyAbstract: The exterior dynamics of black holes has played a major role
in holographic duality, describing the approach to thermal equilibrium
of strongly coupled media. The interior dynamics of black holes in a
holographic setting has, in contrast, been largely unexplored. I will
describe recent work investigating the classical interior dynamics of
various holographic black holes. I will discuss the nature of the
singularity, the absence of Cauchy horizons and a new kind of chaotic
behavior that emerges in the presence of charged scalar fields. 
22/03/2022 2:00 PM(Zoom Link in Abstract)Mikhail Karpukhin (Caltech)Optimization of Laplace and Steklov eigenvalues with applications to minimal surfaces
Abstract: The study of optimal upper bounds for Laplace eigenvalues on closed surfaces is a classical problem of spectral geometry going back to J. Hersch, P. Li and S.T. Yau. Its most fascinating feature is the connection to the theory of minimal surfaces in spheres. Optimization of Steklov eigenvalues is an analogous problem on surfaces with boundary. It was popularised by A. Fraser and R. Schoen, who discovered its connection to the theory of free boundary surfaces in Euclidean balls. Despite many widelyknown empiric parallels, an explicit link between the two problems was discovered only in the last two years. In the present talk, we will show how Laplace eigenvalues can be recovered as certain limits of Steklov eigenvalues and discuss the applications of this construction to the geometry of minimal surfaces. The talk is based on joint works with D. Stern.

15/03/2022 2:00 PMMB503  Maths Seminar RoomSam DolanGravitational selfforce and black hole perturbation theory on Kerr spacetime
I will review approaches to solving the perturbation equations in electromagnetism and linearized gravity on black hole spacetimes in the presence of sources, focussing particularly on recent work in the Lorenz (de Donder) gauge. I will present some partial results and review the challenges remaining. The overall aim is to extend the gravitational selfforce programme to second order in the mass ratio, to accurately model Extreme MassRatio Inspirals for LISA.

22/02/2022 2:00 PMMB503  Maths Seminar RoomArman TaghaviChabertAlmost Robinson geometry
Abstract: Nonshearing congruences of null geodesics on fourdimensional Lorentzian manifolds are fundamental objects of mathematical relativity. Their prominence in exact solutions to the Einstein field equations is supported by major results such as the Robinson, GoldbergSachs and Kerr theorems. Conceptually, they lie at the crossroad between Lorentzian conformal geometry and CauchyRiemann geometry, and are one of the original ingredients of twistor theory.
Identified as involutive totally null complex distributions of maximal rank, such congruences generalise to any even dimensions, under the name of Robinson structures. Nurowski and Trautman aptly described them as Lorentzian analogues of Hermitian structures. In this talk, I will give a survey of old and new results in the field. 
15/02/2022 2:00 PMMB503  Maths Seminar RoomGeorge MavrogiannisLinear and nonlinear wave equations on Schwarzschild de SitterAbstract: "We discuss recent developments in the analysis of linear and nonlinear wave equations on the Schwarzschild de Sitter spacetime, which is a black hole spacetime with a positive cosmological constant. Specifically, we use only time domain methods, as opposed to the previous spectral approach, and give a new proof of exponential decay for the solutions of the linear wave equation and a new proof for the stability of the solutions of the quasilinear wave equation. Trapped null geodesics will make a frequent appearance in this talk."

25/01/2022 3:00 PMMB503 (Zoom Link in Abstract)Debodirna Ghosh (Chennai)Supertranslations at timelike infinity
Abstract: In this talk, I will propose a definition of asymptotic flatness at timelike infinity in four spacetime dimensions. I will also present a detailed study of the asymptotic equations of motion and the action of supertranslations on asymptotic fields. I will then show that the LeeWald symplectic form does not get contributions from future timelike infinity with appropriate boundary conditions. As a result, the “future charges” can be computed on any twodimensional surface surrounding the sources at timelike infinity. Finally, I will present expressions for supertranslation and Lorentz charges.
Zoom: https://qmulacuk.zoom.us/j/82729534665?pwd=UUE3b3pHbDZsSGdhVzF

08/03/2022 2:00 PMMB503  Maths Seminar RoomOlivier Graf (Münster)An L² curvature pinching result for the Euclidean 3disk with applications to general relativity
When studying the Cauchy problem of general relativity we typically obtain L² bounds on the (Ricci) curvature tensor of spacelike hypersurfaces and its derivatives. In many situations it is useful to deduce from these H^{k} bounds that there exists coordinates on the spacelike hypersurface with optimal H^{k+2} bounds on the components of the induced Riemannian metric. The general idea is that this can be achieved using harmonic coordinates  in which the principal terms of the Ricci curvature tensor are the LaplaceBeltrami operators of the metric components  and standard elliptic regularity results. In this talk, I will make this idea concrete in the case of Riemannian 3manifolds with a 2sphere boundary, with Ricci curvature in L² and second fundamental form of the boundary in H^{1/2} both close to their respective Euclidean unit 3disk values. The crux of the proof is a refined Bochner identity with boundary for harmonic functions. The cherry on the cake is that this result does not require any topology assumption on the Riemannian 3manifold (apart from its boundary), and that we obtain  as a conclusion  that it must be diffeomorphic to the 3disk. This talk is based on a result that I obtained in [Global nonlinear stability of Minkowski space for spacelikecharacteristic initial data, Appendix A]

08/02/2022 2:00 PMMB503  Maths Seminar RoomNikolaos Athanasiou (American College of Thessaloniki)A scalecritical trapped surface formation criterion for the EinsteinMaxwell systemAbstract: Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang An, on a scalecritical trapped surface formation criterion for the EinsteinMaxwell system.

01/03/2022 2:00 PMMB503Maths Seminar RoomZoe Wyatt (Cambridge)Stabilising relativistic fluids on slowly expanding cosmological spacetimes
On a background Minkowski spacetime, the relativistic Euler equations are known, for a relatively general equation of state, to admit unstable homogeneous solutions with finitetime shock formation. By contrast, such shock formation can be suppressed on background cosmological spacetimes whose spatial slices expand at an accelerated rate. The critical case of linear, ie zeroaccelerated, spatial expansion, is not as well understood. In this talk, I will present two recent works concerning the relativistic Euler and the EinsteinDust equations for geometries expanding at a linear rate. This is based on joint works with David Fajman, Todd Oliynyk and Max Ofner.

15/02/2022 2:00 PMBOWL Seminar : Zoom (link in abstract)Tristan Ozuch (MIT)Weighted versions of scalar curvature, mass and spin geometry for Ricci flows
With A. Deruelle, we define a Perelman like functional for ALE metrics which lets us study the (in)stability of Ricciflat ALE metrics. With J. Baldauf, we extend some classical objects and formulas from the study of scalar curvature, spin geometry and general relativity to manifolds with densities. We surprisingly find that the extension of ADM mass is the opposite of the above functional introduced with A. Deruelle. Through a weighted Witten’s formula, this functional also equals a weighted spinorial Dirichlet energy on spin manifolds. Ricci flow is the gradient flow of all of these quantities.
Zoom details:
https://ucl.zoom.us/j/95150620185?pwd=THJ5R3B3cjBSclJ5azNXampGOGI0UT09
Meeting ID: 951 5062 0185
Passcode: 956606 
25/01/2022 2:00 PMZoom (link in abstract)Lucas Ambrozio (IMPA)Analogues of Zoll surfaces in minimal surface theory
About 121 years ago, Otto Zoll described a large family of rotationally symmetric Riemannian twodimensional spheres whose geodesics are all closed and have the same period. Since then, a very rich (but yet incomplete) theory developed in order to construct and understand geometries (in a broad sense) with these special geodesic flows, also in higher dimensions. After working on certain systolic questions about minimal twodimensional spheres in threedimensional Riemannian spheres with R. Montezuma (UFC), and motivated by other interesting geometric reasons, I became convinced that another sort of higher dimensional generalisation of Zoll surfaces, within the theory of minimal submanifolds, deserved to be investigated on its own. In this talk, we will report on some of the results we proved about these new objects, including existence results, together with F. Codá Marques (Princeton) and A. Neves (UChicago).
Zoom details:Meeting ID: 951 5062 0185Passcode: 956606 
27/01/2022 2:00 PMMB503 Seminar Room (NOTE: SPECIAL TIME!)Greg FournodavlosThe mysterious nature of the Big Bang singularity
Abstract: 100 years ago, Kasner discovered the first exact cosmological solutions to Einstein's field equations, revealing the presence of a striking new phenomenon, namely, the Big Bang singularity. Since then, it has been the object of study in a great deal of research on general relativity. However, the nature of the 'generic' Big Bang singularity remains a mystery. Rivaling scenarios are abound (monotonicity, chaos, spikes) that make the classification of all solutions a very intricate problem. I will give a historic overview of the subject and describe recent progress that confirms a small part of the conjectural picture.

14/12/2021 2:00 PMZoomIlyas Khan (Oxford)The structure of mean curvature flow translators with finite total curvature
Abstract: In the mean curvature flow, translating solutions are an important model for singularity formation. In this talk, we will consider the class of 2dimensional mean curvature flow translators embedded in R^3 which have finite total curvature and describe their asymptotic structure, which turns out to be highly rigid. I will outline the proof of this asymptotic description, in particular focusing on some novel and unexpected features of the proof.

07/12/2021 2:00 PMMB 503 Seminar RoomLionel Mason (Oxford)The twistor origin of hidden winfinity symmetries in celestial gravity
Abstract: Recently in their celestial holography programme, Strominger and coworkers attempt to provide a holographic description of conventional 4d gravity. In their investigations, they uncovered a hidden winfinity symmetry in their `celestial soft OPEs' for graviton scattering. This talk will explain the origin of this symmetry in terms of old ideas of Newman and Penrose based on lightcone cuts of null infinity and their description in terms of asymptotic twistors and certain sigma models in asymptotic twistor space. W_n symmetries were introduced by Zamolodchikov as higher spin symmetries in 2d conformal field theories. These were given a geometric interpretation for n=infinity as areapreserving diffeomorphisms of the plane. I will explain how the corresponding loop algebra becomes a hidden symmetry of selfdual gravity via Penrose's nonlinear graviton construction. The action of this symmetry on the treelevel Smatrix of full gravity beyond the selfdual sector will then be obtained from its action on a sigma model in the asymtotic twistor space of a general spacetime. This talk is based on https://arxiv.org/abs/2110.06066 and https://arxiv.org/abs/2103.16984.

30/11/2021 3:00 PMMB 503 Seminar RoomMatthew Schrecker (UCL)Existence theory and Newtonian limit for 1D relativistic Euler equations
Abstract: After a brief discussion of the problem of relativistic fluids, I will talk about the 1D compressible, isentropic Euler equations in special relativity. In recent work, G.Q. Chen and I have shown the existence of global entropy solutions to this system through a compensated compactness framework, which I will outline in this talk. We also demonstrate the convergence of relativistic solutions to their classical (Newtonian) counterparts, and so, in the final portion of my talk, I will briefly outline how this is achieved.

23/11/2021 2:00 PMMB503 Seminar RoomAlex McGill (QMUL)Unique Continuation for Waves and Local AdS Rigidity
Abstract: In the context of holography, one would like to establish correspondence statements between asymptotically antide Sitter (aAdS) solutions of the Einsteinvacuum equations and suitable ‘data’ on the conformal boundary. To this end, progress has been made in the Riemannian (Biquard ‘08) and Stationary Lorentzian (ChruścielDelay ‘11) cases. I will present recent unique continuation results for wave equations on aAdS backgrounds which lay the groundwork for progress in the nonstationary setting. In particular, I will describe how these preliminary results lead to a rigidity statement for locally AdS spacetimes based around conditions on the boundary data. This talk involves joint work with Arick Shao.

16/11/2021 2:00 PMZoomChristina Sormani (CUNY)VF convergence and scalar curvature
Abstract: We will present a collection of conjectures formulated with Gromov and other members of our IAS Emerging Topics Working Group on the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We will survey results in special cases and present key theorems concerning volume preserving intrinsic flat convergence that have been applied to prove these special cases. For a complete list of papers about intrinsic flat convergence see here.
Zoom details:https://ucl.zoom.us/j/92705362785?pwd=VGtKdVBuQzRFRVlXYTdXL1VDOURPUT09
Meeting ID: 927 0536 2785Passcode: 873569

16/11/2021 3:00 PMMB 503 Seminar RoomHameed Masaood (Cambridge)A scattering theory for linearised gravity on the Schwarzschild black hole exterior.Abstract: I will first describe how the energy conservation associated to the ReggeWheeler equation can be used together with the Chandrasekhar transformations to construct a scattering theory for the spin \pm2 Teukolsky equations on the Schwarzschild black hole. I will then describe how the results on the Teukolsky equations can be upgraded to construct a scattering theory for the Einstein equations when linearised in a double null gauge against a Schwarzschild background. In particular, I will describe how the BMS groups at past and future null infinity can be related in the context of the scattering problem.

09/11/2021 2:00 PMMB Seminar Room 503Toby Wiseman (Imperial)Surprising similarities for vacuum energy in holographic and free CFTs in (2 + 1) dimensions
Abstract:
Both in the context of QCD and CMT the AdSCFT correspondence has been used to describe the behaviour of strongly coupled field theories via a classical gravity dual. While this gives a beautiful geometrization of certain problems in strongly coupled theories, an important long standing question is how similar the quantitative behaviour of holographic theories is to the usual QFTs we are typically interested in. We address this by studying a universal property of QFTs, the dependence of vaccum energy on the curvature of space, focussing on (2+1)dimensions. I will detail how to numerically compute this Casimir energy in the free field setting, and how to compute it in the holographic context. We will then see a very surprising similarity in the detailed behaviour between holographic theories and free CFTs, particularly the free Dirac theory. We will also discuss some interesting geometric constraints on this energy in the holographic case both in vacuum and also at finite temperature, that arise from bulk considerations. Together with our numerical free field calculations this motivates an interesting conjecture for free theories. 
26/10/2021 2:00 PMZoomHarvey Reall (Cambridge)Causality in gravitational theories with second order equations of motion
Abstract:
I will discuss diffeomorphism invariant theories of gravity coupled to matter, with second order equations of motion. This includes Lovelock and Horndeski theories, as well as some effective field theories which include 4derivative corrections to conventional 2derivative theories. In such theories, generically causality is not determined by the null cone of the metric. I will describe a method for studying causality in these theories in a gaugeinvariant way. For the class of theories with a single scalar field, I will present an explicit characterization of the causal cone in an arbitrary background. There is an interesting analogy with the cone associated with wave propagation in certain anisotropic elastic solids. 
02/11/2021 2:00 PMZoomThomas Koerber (Vienna)Foliations of Asymptotically Flat 3Manifolds by Stable Constant Mean Curvature Spheres
Stable constant mean curvature spheres encode important information on the asymptotic geometry of initial data sets for isolated gravitational systems. In this talk, I will present a short new proof (joint with M. Eichmair) based on LyapunovSchmidt reduction of the existence of an asymptotic foliation of such an initial data set by stable constant mean curvature spheres. In the case where the scalar curvature is nonnegative, our method also shows that the leaves of this foliation are the only large stable constant mean curvature spheres that enclose the center of the initial data set.

19/10/2021 2:00 PMZoomChristoph Böhm (Münster)Noncompact Einstein manifolds with symmetry
Abstract: For Einstein manifolds with negative scalar curvature admitting an isometric action of a Lie group G with compact, smooth orbit space, we show the following rigidity result:
The nilradical N of G acts polarly and the Norbits are locally isometric to a nilsoliton.Applications will be discussed. This is joint work with R. Lafuente.
Zoom details:https://ucl.zoom.us/j/92705362785?pwd=VGtKdVBuQzRFRVlXYTdXL1VDOURPUT09
Meeting ID: 927 0536 2785Passcode: 873569

05/10/2021 2:00 PMZoomMartin Taylor (Imperial College)The nonlinear stability of the Schwarzschild family of black holes
I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes. The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family. This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.
Zoom details:https://ucl.zoom.us/j/92705362785?pwd=VGtKdVBuQzRFRVlXYTdXL1VDOURPUT09
Meeting ID: 927 0536 2785Passcode: 873569

30/11/2021 2:00 PMZoomPanagiota Daskalopoulos (Columbia)TBA

15/06/2021 4:00 PMZoomLaura Fredrickson (Oregon)ALG Gravitational Instantons and Hitchin Moduli Spaces
Abstract: Fourdimensional complete hyperkaehler manifolds can be classified into ALE, ALF, ALG, ALG*, ALH, ALH* families. It has been conjectured that every ALG or ALG* hyperkaehler metric can be realized as a 4d Hitchin moduli space. I will describe ongoing work with Rafe Mazzeo, Jan Swoboda, and Hartmut Weiss to prove a special case of the conjecture, and some consequences. The hyperkaehler metrics on Hitchin moduli spaces are of independent interest, as the physicists Gaiotto—Moore—Neitzke give an intricate conjectural description of their asymptotic geometry.

08/06/2021 1:45 PMZoomAnna Siffert (Münster)Construction of explicit pharmonic functions
Abstract: The study of pharmonic functions on Riemannian manifolds has invoked the interest of mathematicians and physicists for nearly two centuries. Applications within physics can for example be found in continuum mechanics, elasticity theory, as well as twodimensional hydrodynamics problems involving Stokes flows of incompressible Newtonian fluids.
In my talk I will focus on the construction of explicit pharmonic functions on rankone Lie groups of Iwasawa type. This joint work with Sigmundur Gudmundsson and Marko Sobak.

01/06/2021 1:45 PMZoomHansJoachim Hein (Münster)Smooth asymptotics for collapsing CalabiYau metrics
Abstract: I will present recent joint work with Valentino Tosatti in which we obtain a complete asymptotic expansion (locally uniformly away from the singular fibers) of CalabiYau metrics collapsing along a holomorphic fibration of a fixed compact CalabiYau manifold. The result is weaker than a standard asymptotic expansion in that the coefficient functions might still depend on the small parameter in some unknown way in the base variables. However, it is far stronger in that all terms including the remainder at each order are proved to be uniformly bounded in C^k for all k. We also calculate the first nontrivial coefficient in terms of the KodairaSpencer forms of the fibration.

25/05/2021 1:45 PMZoomCostante Bellettini (UCL)Existence of hypersurfaces with prescribed meancurvature
Abstract: Let N be a compact Riemannian manifold of dimension 3 or higher, and g a Lipschitz nonnegative (or nonpositive) function on N. We prove that there exists a closed hypersurface M whose mean curvature attains the values prescribed by g (joint work with Neshan Wickramasekera, Cambridge). Except possibly for a small singular set (of codimension 7 or higher), the hypersurface M is C^2 immersed and twosided (it admits a global unit normal); the scalar mean curvature at x is g(x) with respect to a global choice of unit normal. More precisely, the immersion is a quasiembedding, namely the only nonembedded points are caused by tangential selfintersections: around such a nonembedded point, the local structure is given by two disks, lying on one side of each other, and intersecting tangentially (as in the case of two spherical caps touching at a point). A special case of PMC (prescribedmeancurvature) hypersurfaces is obtained when g is a constant, in which the above result gives a CMC (constantmeancurvature) hypersurface for any prescribed value of the mean curvature. The construction of M is carried out largely by means of PDE principles: (i) a minmax for an Allen–Cahn (or ModicaMortola) energy, involving a parameter that, when sent to 0, leads to an interface from which the desired PMC hypersurface is extracted; (ii) quasilinear elliptic PDE and geometricmeasuretheory arguments, to obtain regularity conclusions for said interface; (iii) parabolic semilinear PDE (together with specific features of the AllenCahn framework), to tackle cancellation phenomena that can happen when sending to 0 the AllenCahn parameter.

18/05/2021 1:45 PMZoomYevgeny Liokumovich (Toronto)Foliations of 3manifolds of positive scalar curvature by surfaces of controlled size
Abstract : Let M be a compact 3manifold with scalar curvature at least 1. We show that there exists a Morse function f on M, such that every connected component of every fiber of f has genus, area and diameter bounded by a universal constant. The proof uses MinMax theory and Mean Curvature Flow. This is a joint work with Davi Maximo. Time permitting, I will discuss a related problem for macroscopic scalar curvature in metric spaces (joint with Boris Lishak, Alexander Nabutovsky and Regina Rotman).

09/03/2021 6:00 PMZoomRichard Bamler (UC Berkeley)Compactness and partial regularity theory of Ricci flows in higher dimensions
COMPACTNESS AND PARTIAL REGULARITY THEORY OF RICCI FLOWS IN HIGHER DIMENSIONS
We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural noncollapsing condition, this limiting flow is smooth on the complement of a singular set of parabolic codimension at least 4. We furthermore obtain a stratification of the singular set with optimal dimensional bounds depending on the symmetries of the tangent flows. Our methods also imply the corresponding quantitative stratification result and the expected L^pcurvature bounds.
As an application we obtain a description of the singularity formation at the first singular time and a longtime characterization of immortal flows, which generalizes the thickthin decomposition in dimension 3. We also obtain a backwards pseudolocality theorem and discuss several other applications.

02/03/2021 1:45 PMZoomGábor Székelyhidi (Notre Dame)Uniqueness of certain cylindrical tangent cones
UNIQUENESS OF CERTAIN CYLINDRICAL TANGENT CONES
Leon Simon showed that if an area minimizing hypersurface
admits a cylindrical tangent cone of the form C x R, then this tangent
cone is unique for a large class of minimal cones C. One of the
hypotheses in this result is that C x R is integrable and this
excludes the case when C is the Simons cone over S^3 x S^3. The main
result in this talk is that the uniqueness of the tangent cone holds
in this case too. The new difficulty in this nonintegrable situation
is to develop a version of the LojasiewiczSimon inequality that can
be used in the setting of tangent cones with nonisolated
singularities. 
30/03/2021 1:45 PMZoomIlaria Mondello (ParisEst Créteil)Limits of manifolds with a Kato bound on the Ricci curvature
LIMITS OF MANIFOLDS WITH A KATO BOUND ON THE RICCI CURVATURE
Starting from Gromov precompactness theorem, a vast theory about the structure of limits of manifolds with a lower bound on the Ricci curvature has been developed thanks to the work of J. Cheeger, T.H. Colding, M. Anderson, G. Tian, A. Naber, W. Jiang. Nevertheless, in some situations, for instance in the study of geometric flows, there is no lower bound on the Ricci curvature. It is then important to understand what happens when having a weaker condition.
In this talk, we present new results about limits of manifolds with a Kato bound on the negative part of the Ricci tensor. Such bound is weaker than the previous L^p bounds considered in the literature (P. Petesern, G. Wei, G. Tian, Z. Zhang, C. Rose, L. Chen, C. Ketterer…). In the noncollapsing case, we recover part of the regularity theory that was known in the setting of Ricci lower bounds: in particular, we obtain that all tangent cones are metric cones, a stratification result and volume convergence to the Hausdorff measure. After presenting the setting and main theorem, we will focus on proving that tangent cones are metric cones, and in particular on the study of the appropriate monotone quantities that leads to this result.

04/05/2021 1:45 PMZoomRobert Haslhofer (Toronto)Mean curvature flow through necksingularities
In this talk, I will explain our recent work showing that mean curvature flow through necksingularities is unique. The key is a classification result for ancient asymptotically cylindrical flows that describes all possible blowup limits near a necksingularity. In particular, this confirms Ilmanen’s meanconvex neighborhood conjecture, and more precisely gives a canonical neighborhood theorem for necksingularities. Furthermore, assuming the multiplicityone conjecture, we conclude that for embedded twospheres mean curvature flow through singularities is wellposed. The twodimensional case is joint work with Choi and Hershkovits, and the higherdimensional case is joint with Choi, Hershkovits and White.

11/05/2021 1:45 PMZoomGilles Carron (Nantes)Rigidity of the Euclidean heat kernel
RIGIDITY OF THE EUCLIDEAN HEAT KERNEL
It is a joint work with David Tewodrose (Bruxelles) https://arxiv.org/abs/1912.10759
I will explain that a metric measure space with Euclidean heat kernel is Euclidean. An almost rigidity result comes then for free, and this can be used to give another proof of Colding’s almost rigidity for complete manifold with non negative Ricci curvature and almost Euclidean growth.

23/03/2021 1:45 PMZoomYi Lai (UC Berkeley)A family of 3d steady gradient solitons that are flying wings
We find a family of 3d steady gradient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing, we show that the scalar curvature does not vanish at infinity. The 3d flying wings are collapsed. For dimension n ≥ 4, we find a family of Z2 × O(n − 1)symmetric but nonrotationally symmetric ndimensional steady gradient solitons with positive curvature operator. We show that these solitons are noncollapsed.

16/02/2021 1:45 PMZoomClaude Lebrun (Stonybrook)AntiSelfDual 4Manifolds, QuasiFuchsian Groups, and AlmostKähler Geometry
Abstract: It is known that the almostKähler antiselfdual metrics on a given 4manifold sweep out an open subset in the moduli space of antiselfdual metrics. However, we show by example that this subset is not generally closed, and does not always sweep out entire connected components in the moduli space. The construction hinges on an unexpected link between harmonic functions on certain hyperbolic 3manifolds and selfdual harmonic 2forms on associated 4manifolds.

02/02/2021 1:45 PMZoomChao Li (Princeton)Scalar curvature on aspherical manifolds
Abstract: It has been a classical question which manifolds admit Riemannian metrics with positive scalar curvature. I will first review some history of this question, and present some recent progress, ruling out positive scalar curvature on closed aspherical manifolds of dimensions 4 and 5 (as conjectured by SchoenYau and by Gromov). I will also discuss some related questions including the Urysohn width inequalities on manifolds with scalar curvature lower bounds. This talk is based on joint work with Otis Chodosh.
Zoom details:
https://ucl.zoom.us/j/97740010241?pwd=RElWTDQvSUFiTWNRVFpIOEMyNCtKUT09Meeting ID: 977 4001 0241
Passcode: 261438 
16/03/2021 1:45 PMZoomRobin Neumayer (Northwestern)d_p Convergence and epsilonregularity theorems for entropy and scalar curvature lower bounds
In this talk, we consider Riemannian manifolds with almost nonnegative scalar curvature and Perelman entropy. We establish an epsilonregularity theorem showing that such a space must be close to Euclidean space in a suitable sense. Interestingly, such a result is false with respect to the GromovHausdorff and Intrinsic Flat distances, and more generally the metric space structure is not controlled under entropy and scalar lower bounds. Instead, we introduce the notion of the d_p distance between (in particular) Riemannian manifolds, which measures the distance between W^{1,p} Sobolev spaces, and it is with respect to this distance that the epsilon regularity theorem holds. We will discuss various applications to manifolds with scalar curvature and entropy lower bounds, including a compactness and limit structure theorem for sequences, a uniform L^infinity Sobolev embedding, and a priori L^p scalar curvature bounds for p<1 This is joint work with ManChun Lee and Aaron Naber.

29/01/2021 2:00 PMZoomAdrian Butscher (Autodesk, Toronto, Canada)Topology Optimization
Although the words "Topology" and "Optimization" make perfect sense to a mathematician, the compound term "Topology Optimization" might raise eyebrows. Nevertheless, Topology Optimization is a welldefined concept in the field of computational design in engineering. In
computational design, the engineer relies on algorithms to automatically generate solutions to engineering design problems. In the case of Topology Optimization, this means to generate a shape (a.k.a. domain with piecewisesmooth boundary) that fulfills an engineering task (e.g. transmits torque) with optimal performance (e.g. is stiff and lightweight). I will explain this concept in more detail, from the mathematical formulation and the numerical
implementation to the application in realworld engineering design scenarios.
Bio 
23/02/2021 1:45 PMZoomEleonora Di Nezza (Ecole Polytechnique)Families of KählerEinstein metrics
Abstract:
In a lot of geometric situation we need to work with families of varieties. In this talk we focus on families of singular KählerEinstein metric. In particular we study the case of a family of Kähler varieties and we develop the first steps of pluripotential theory in family, which will allow us to have a control on the C^0 estimate when the complex structure varies. This type of result will be applied in different geometric contexts. This is a joint work with V. Guedj and H. Guenancia.

26/01/2021 1:45 PMZoomTheodora Bourni (Tennessee)Ancient solutions to mean curvature flow
Mean curvature flow (MCF) is the gradient flow of the area functional; it moves the surface in the direction of steepest decrease of area. An important motivation for the study of MCF comes from its potential geometric applications, such as classification theorems and geometric inequalities. MCF develops “singularities” (curvature blowup), which obstruct the flow from existing for all times and therefore understanding these high curvature regions is of great interest. This is done by studying ancient solutions, solutions that have existed for all times in the past, and which model singularities. In this talk we will discuss their importance and ways of constructing and classifying such solutions. In particular, we will focus on “collapsed” solutions and construct, in all dimensions n>=2, a large family of new examples, including both symmetric and asymmetric examples, as well as many eternal examples that do not evolve by translation. Moreover, we will show that collapsed solutions decompose “backwards in time” into a canonical configuration of Grim hyperplanes which satisfies certain necessary conditions. This is joint work with Mat Langford and Giuseppe Tinaglia.

19/01/2021 1:45 PMZoomFritz Heismayr (UCL)A Bernstein theorem for twovalued minimal graphs in dimension four
The Bernstein theorem is a classical result for minimal graphs. It states that a globally defined solution of the minimal surface equation on $R^n$ must be linear, provided the dimension is small enough. We present an analogous theorem for twovalued minimal graphs, valid in dimension four. By definition twovalued functions take values in the unordered pairs of real numbers; they arise as the local model of branch point singularities. The plan is to juxtapose this with the classical singlevalued theory, and explain where some of the difficulties emerge in the twovalued setting.

15/12/2020 1:45 PMZoomCasey Kelleher (Princeton)Gap Theorem Results in YangMills TheoryAbstract: We discuss results concerning the space of YangMills connections on vector bundles over compact 4dimensional Riemannian manifolds. In particular, we discuss a conformally invariant gap theorem for YangMills connections obtained by exploiting an associated Yamabetype problem. We also discuss a bound for the index in terms of its energy which is conformally invariant, which captures the sharp growth rate. This is joint work with M. Gursky and J. Streets.
https://ucl.zoom.us/j/91921950801?pwd=bnEwUWsrODMybEUwR01GNURZcVAvQT09
Meeting ID: 919 2195 0801Passcode: 9f$8mt 
08/12/2020 1:45 PMZoomNikon Kurnosov (UCL)Deformation theory and geometry of BogomolovGuan manifolds
Abstract: In 1994, Guan published a series of papers constructing nonKähler holomorphic symplectic manifolds, challenging a conjecture by Todorov. These examples, called now BG manifolds were given a more transparent presentation by Bogomolov in '96, which emphasizes the analogy with the KodairaThurston example of nonKähler symplectic surfaces. We will discuss some important properties of BG manifolds: deformation theory, which is quite similar to that of the hyperKaehler case, algebraic reduction and submanifolds.

24/11/2020 3:00 PMZoomTracey Balehowsky (Helsinki)Determining a Lorentzian metric from the sourcetosolution map for the relativistic Boltzmann equationAbstract: In this talk, we consider the following problem: Given the sourcetosolution map for a relativistic Boltzmann equation on a neighbourhood $V$ of a timelike observer in a Lorentzian spacetime $(M,g)$ and knowledge of $g_V$, can we determine (up to diffeomorphism) the spacetime metric $g$ on the domain of causal influence for the set $V$?We will show that the answer is yes. The problem we consider is a socalled inverse problem. We will review some results and techniques developed in the study of inverse problems similar to ours. We will also introduce the relativistic Boltzmann equation and comment on existence of solutions to this PDE given some initial data. We then will sketch the key ideas of the proof of our result. One such key point is that the nonlinear term in the relativistic Boltzmann equation which describes the behaviour of particle collisions captures information about a sourcetosolution map for a related linearized problem. We use this relationship together with an analysis of the behaviour of particle collisions by classical microlocal techniques to determine the set of locations in $V$ where we first receive light particle signals from collisions in the unknown domain. From this data we are able to parametrize the unknown region and determine the metric.Huy The Nguyen is inviting you to a scheduled Zoom meeting.
Topic: QMUL Geometry and Analysis Seminar
Time: Nov 24, 2020 03:00 PM London
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24/11/2020 1:45 PMZoomDario Beraldo (UCL)On the geometry of Bun_G near infinity
Let Bun_G be the moduli stack of Gbundles on a compact Riemann surface. After reviewing (and motivating) the notion of “temperedness” appearing in the geometric Langlands program, I will discuss the proof of a conjecture of Gaitsgory stating that the constant Dmodule on Bun_G is antitempered. No prior familiarity with geometric Langlands will be assumed; rather, I’ll emphasize some key ingredients that might be of broader interest: a Serre duality in an unusual context and various cohomology vanishing computations.

17/11/2020 1:45 PMZoomJeanPierre Demailly (Institut Fourier)HermitianYangMills Approach to the Conjecture Of Griffiths on the Positivity of Ample Vector Bundles
Abstract: Given a vector bundle of arbitrary rank with ample determinant line
bundle on a projective manifold, we propose a new elliptic system of differential equations of HermitianYangMills type for the curvature tensor. The system is designed so that solutions provide Hermitian metrics with positive curvature in the sense of Griffiths – and even in the dual Nakano sense. As a consequence, if an existence result could be obtained for every ample vector bundle, the Griffiths conjecture on the equivalence between ampleness and positivity of vector bundles would be settled. Another outcome of the approach is a new concept of volume for vector bundles. 
01/12/2020 1:45 PMZoomJasmin Hörter (Karlsruhe)Limits of $\epsilon$harmonic maps
In 1981 Sacks and Uhlenbeck introduced their famous alphaapproximation of the Dirichlet energy for maps from surfaces and showed that critical points converge to a harmonic map (away from finitely many points). Now one can ask whether every harmonic map is captured by this limiting process. Lamm, Malchiodi and Micallef answered this for maps from the two sphere into the two sphere and showed that the SacksUhlenbeck method produces only constant maps and rotations if the energy lies below a certain threshold. We investigate the same question for the epsilonapproximation of the Dirichlet energy.
Joint work with Tobias Lamm and Mario Micallef.

10/11/2020 1:45 PMZoomTristan OzuchMeersseman (MIT)Higher order obstructions to the desingularization of Einstein metrics
Abstract: We exhibit new obstructions to the desingularization of Einstein metrics in dimension 4. These obstructions are specific to the compact situation and raise the question of whether or not a sequence of Einstein metrics degenerating while bubbling out gravitational instantons has to be KählerEinstein. We then test these obstructions to discuss the possibility of producing a Ricciflat but not Kähler metric by the promising desingularization configuration proposed by Page in 1981.

03/11/2020 1:45 PMZoomMarco Guaraco (Imperial College London)Title: Multiplicity one of generic stable AllenCahn minimal hypersurfaces
Abstract: AllenCahn (AC) minimal hypersurfaces are limits of nodal sets of solutions to the AC equation. An important problem is to understand the local picture of this convergence. For instance, can we avoid the situation in which the nodal set looks like a multigraph over the limit hypersurface? General examples of this phenomenon, known as “multiplicity” or "interface foliation”, exist when the limit hypersurface is unstable. Together with A. Neves and F. Marques we proved that, generically and in all dimensions, these are the only possible examples of interface foliation, i.e. generic stable AC minimal hypersurfaces can only occur with multiplicity one. We will discuss this and other topics.

27/10/2020 1:45 PMZoomColleen Robles (Duke)Completions of Period Mappings
It’s a long standing problem in Hodge theory to complete the image of a period map. The latter arise in the study of algebraic moduli, and are proper holomorphic maps into locally homogeneous spaces that are subject to a differential constraint. I’ll give a survey of the problem and then describe recent progress, with an emphasis on the role of complex geometry and Lie theory. Joint with Mark Green and Phillip Griffiths.

20/10/2020 1:45 PMZoomOtis Chodosh (Stanford)Generic Regularity of minmax hypersurfaces in eight dimensions
Abstract: I will discuss recent work with Yevgeny Liokumovich and Luca Spolaor concerning generic regularity of minmax minimal hypersurfaces in the first dimension that they might be singular.

13/10/2020 1:45 PMZoomDaniel Stern (Chicago)Constructing minimal submanifolds via gauge theory
Abstract: The selfdual YangMillsHiggs (or GinzburgLandau) functionals are a natural family of energies associated to sections and metric connections of Hermitian line bundles, whose critical points (particularly those satisfying a firstorder system known as the “vortex equations” in the Kahler setting) have long been studied as a basic model problem in gauge theory. In this talk, we will discuss joint work with Alessandro Pigati characterizing the behavior of critical points associated to line bundles over manifolds of arbitrary dimension. We show in particular that critical points give rise to minimal submanifolds of codimension two in certain natural scaling limits, and use this information to provide new constructions of codimensiontwo minimal varieties in arbitrary Riemannian manifolds.

06/10/2020 12:45 PMZoomCARLO SCARPA (SISSA, TRIESTE)THE HITCHINCSCK SYSTEM
A classic result in the study of Kähler metrics with special curvature properties is that the cscK equation can be realized as the moment map equation for an infinitedimensional Kähler reduction. We present a natural hyperkähler extension of this moment map picture, obtaining a new system of equations reminiscent of Hitchin’s equations for Higgs bundles. We will discuss some recent existence results, particularly obstructions to solutions to the problem.
To keep uptodate with the schedule, and to receive the Zoom link for each talk, you can subscribe to the B.O.W.L. mailing list on the page http://geometry.ulb.ac.be/bowl/

29/09/2020 1:45 PMZoom (http://geometry.ulb.ac.be/bowl/)Goncalo Oliveira (Fluminese)G2monopoles
G2MONOPOLES
This talk is aimed at reviewing what is known about G2monopoles and motivate their study. After this, I will mention some recent results obtained in collaboration with Ákos Nagy and Daniel Fadel which investigate the asymptotic behavior of G2monopoles. Time permitting, I will mention a few possible future directions regarding the use of monopoles in G2geometry.

29/04/2020 3:30 PMZoom Meeting ID: 967 5743 6470 Password: 059133Katy Clough (Oxford)Searching for light dark matter in strong gravity environments
(This seminar is held jointly with the Relativity and Cosmology Seminar)
With no discovery of WIMPs to date, attention is turning towards lighter mass (sub eV) candidates for dark matter such as the axion. I will discuss their wavelike behaviour, and highlight the challenges in detecting signatures from such light particles in strong gravity environments. In particular, I will consider what types of dark matter structures may realistically form, and how their imprints could appear in gravitational channels. Such observations may be the only way to confirm the nature of dark matter, in the absence of any couplings to standard model particles. 
07/04/2020 3:00 PMOnline (Microsoft Teams)Vaibhav Jena (QMUL)Carleman estimates and interior controllability for wave equations
(This Geometry and Analysis Webinar is held online on MS Teams.)
A system is called controllable if we can drive its solution from a given initial state to a chosen final state, using a suitable control function. One of the techniques for showing controllability is to use Carleman estimates, which are used for proving unique continuation results. In this talk, we will present a novel Carleman estimate for wavetype operators in (m, n) dimension. A special case of this estimate will then be used to show improved interior controllability results for the ndimensional wave equation with lower order terms. 
24/03/2020 3:00 PMOnline (Microsoft Teams)Juan Valiente Kroon (QMUL)Total characteristics and the conformal field equations
(This Geometry and Analysis Webinar is held online on MS Teams.)
It is well known that the restriction of a symmetric hyperbolic system to one of its characteristic hypersurfaces gives rise to a set of (intrinsic) transport equations. Total characteristics are an extreme case of this: on one such hypersurface, the full symmetric hyperbolic evolution system reduces to transport equations. Total characteristics arise naturally in the study of the conformal structure of spacetimes —most notably, in the analysis of the Einstein equations in a neighbourhood of spatial infinity. Similar totally characteristic structures naturally arise in the study of the conformal structure of (a) asymptotically flat extremal black holes; (b) de Sitterlike black hole spacetimes. 
31/03/2020 3:00 PMOnline (Microsoft Teams)Florian LitzingerOptimal regularity for Pfaffian systems and the fundamental theorem of surface theory(This Geometry and Analysis Webinar is held online on MS Teams.)The fundamental theorem of surface theory asserts the existence of a
surface immersion with prescribed first and second fundamental forms that satisfy the Gauss–Codazzi–Mainardi equations. Its proof is based on the solution of a Pfaffian system and an application of the Poincaré lemma. Consequently, the regularity of the resulting immersion crucially depends on the regularity of the solution of the corresponding Pfaffian system. This talk shall briefly review both the classical smooth case and the existing regularity theory and then introduce a recent extension to the optimal regularity. 
31/03/2020 2:00 PMMathematics Building, Room MB503Lashi Bandara (Potsdam)Postponed (Boundary value problems for general firstorder elliptic differential operators)
The index theorem for compact manifolds with boundary, established by AtiyahPatodiSinger in 1975, is considered one of the most significant mathematical achievements of the 20th century.
An important and curious fact is that local boundary conditions are topologically obstructed for index formulae and nonlocal boundary conditions lie at the heart of this theorem.
Consequently, this has inspired the study of boundary value problems for firstorder elliptic differential operators by many different schools, with a class of induced boundary operators taking centre stage in establishing nonlocal boundary conditions.
The work of Bär and Ballmann from 2012 is a modern and comprehensive framework that is useful to study elliptic boundary value problems for firstorder elliptic operators on manifolds with compact and smooth boundary.
As in the work of AtiyahPatodiSinger, a fundamental assumption in BärBallmann is that the induced operator on the boundary can be chosen selfadjoint.
All Diractype operators, which in particular includes the HodgeDirac operator as well as the AtiyahSinger Dirac operator, are captured via this framework.
In contrast to the APS index theorem, which is essentially restricted to Diractype operators, the earlier index theorem of AtiyahSinger from 1968 on closed manifolds is valid for general firstorder elliptic differential operators.
There are important operators from both geometry and physics which are more general than those captured by the stateoftheart for BVPs and index theory.
A quintessential example is the RaritaSchwinger operator on 3/2spinors, which arises in physics for the study of the socalled delta baryons.
A fundamental and seemingly fatal obstacle to study BVPs for such operators is that the induced operator on the boundary may no longer be chosen selfadjoint, even if the operator on the interior is symmetric.
In recent work with Bär, we extend the BärBallmann framework to consider general firstorder elliptic differential operators by dispensing with the selfadjointness requirement for induced boundary operators.
Modulo a zeroth order additive term, we show every induced boundary operator is a bisectorial operator via the ellipticity of the interior operator.
An essential tool at this level of generality is the bounded holomorphic functional calculus, coupled with pseudodifferential operator theory, semigroup theory as well as methods arising from the resolution of the Kato square root problem.
This perspective also paves way for studying noncompact boundary, Lipschitz boundary, as well as boundary value problems in the L^p setting. 
24/03/2020 4:39 PMMathematics Building, Room MB503Stephen Lynch (Tübingen)Postponed (A fully nonlinear flow of threeconvex hypersurfaces)
We will discuss a fully nonlinear geometric flow of threeconvex hypersurfaces, where the normal speed at each point of the solution is given by a concave function of the second fundamental form. Threeconvexity means that at each point, the sum of the smallest three principal curvatures is positive. The flow smoothly deforms compact threeconvex initial hypersurfaces until their curvature becomes unbounded. Our main result is a convexity estimate, which says that where the curvature is very large, the second fundamental form is approximately nonnegative. Such an estimate is known to hold for meanconvex mean curvature flow, and for a large class of fully nonlinear flows where the speed function is convex. For concave speeds, previous results of this kind assume twoconvexity.

26/02/2020 3:30 PMRoom 516, G.O. Jones BuildingKaty Clough (Oxford)(Postponed)
(This seminar is held jointly with the Relativity and Cosmology Seminar)

10/03/2020 3:00 PMMathematics Building, Room MB503Shengwen Wang (QMUL)Improved convergence of low entropy AllenCahn flows to mean curvature flow and curvature estimates.
Abstract: The parabolic AllenCahn equations is the gradient flow of phase transition energy and can be viewed as a diffused version of mean curvature flows of hypersurfaces. It has been known by the works of Ilmanen and Tonegawa that the energy densities of the AllenCahn flows converges to mean curvature flows in the sense of varifold and the limit varifold is integer rectifiable. It is not known in general whether the transition layers have higher regularity of convergence yet. In this talk, I will report on a joint work with Huy Nguyen that under the low entropy condition, the convergence of transition layers can be upgraded to C^{2,\alpha} sense. This is motivated by the work of WangWei and ChodoshMantoulidis in elliptic case that under the condition of stability, one can upgrade the regularity of convergence.

18/02/2020 3:00 PMMathematics Building, Room MB503Catalin Badea (University of Lille, France)Kazhdan sets and constants: some unconventional applications
Kazhdan's Property (T) for topological groups has found applications in domains as diverse as group theory, differential geometry, potential theory, operator algebras, combinatorics and computer science. The aim of my talk, which is intended for a wide audience, is to introduce the notions of Kazhdan sets and Kazhdan constants, and to present some unconventional applications in harmonic analysis, ergodic theory and dynamical systems. A problem related to Furstenberg's $\times 2$$\times 3$ conjecture will be also discussed.

11/02/2020 3:00 PMMathematics Building, Room MB503Christopher Kauffman (Imperial)Global Stability for the massless EinsteinMaxwellKleinGordon system in harmonic coordinatesWe consider the massless EinsteinMaxwellKleinGordon system in 1+3 dimensions. It is known that for the Einstein vacuum equations in wave coordinates, the light cones of the solution metric will asymptotically behave like those of Schwarzschild. We outline a proof of this result generalized to solutions of Einsteinfield systems where the energymomentum tensor satisfies certain integrated and energy bounds. Given this, we can select a system of generalized wave coordinates adapted to the initial ADM mass, which more precisely capture the nature of the weak null condition for the MaxwellKleinGordon system. We can use these coordinates to more precisely capture behavior of solutions of the MaxwellKleinGordon system in this background, and consequently solve the coupled system. This is based on joint work with Hans Lindblad.

28/01/2020 10:00 AMG.O. Jones, Room 410(Multiple speakers)MiniWorkshop on Wave Equations (2829 January)
Miniworkshop website: http://www.maths.qmul.ac.uk/~shao/events/ws2020

03/03/2020 3:00 PMMathematics Building, Room MB503Alexis Michelat (CNRSUniversité Pierre et Marie CurieUniversité Paris Diderot)On the Morse Index of Branched Willmore Spheres
Inversions of complete minimal surfaces with finite total curvature in threespace are known to be critical points of the Willmore energy, or of the integral of mean curvature squared, a conformal invariant first studied by Poisson and Sophie Germain in the beginning of the 19th century. Furthermore, Bryant showed that Willmore immersions of genus 0, also called Willmore spheres, are all inversions of minimal surfaces. More generally, we extended Bryant’s result and showed in particular with Tristan Rivière that branched Willmore spheres arising as weak limits of bubbles of immersions are conformally minimal. We will show that the Morse index of conformally minimal Willmore surfaces in threespace is equal to the index of a canonically associated matrix whose dimension is equal to the number of ends of the dual minimal surface.

21/01/2020 3:00 PMMathematics Building, Room MB503Dongbing Zha (Donghua University)On onedimension quasilinear wave equations with null conditionsWe show that onedimension systems of quasilinear wave equations with null conditions admit global classical solutions for small initial data. This result extends Luli, Yang and Yu's work [G. Luli, S. Yang, P. Yu, On onedimension semilinear wave equations with null conditions, Adv. Math.329 (2018) 174188] from the semilinear case to the quasilinear case. Furthermore, we also prove that the global solution is asymptotically free in the energy sense. In order to achieve these goals, we will employ Luli, Yang and Yu's weighted energy estimates with positive weights, introduce some spacetime weighted energy estimates and pay some special attentions to the highest order energies, then use some suitable bootstrap process to close the argument.

10/12/2019 3:00 PMMathematics Building, Room: MB503Oleg Karpenkov (Liverpool)Geometry of continued fractions
In this talk we introduce a geometrical model of continued fractions
and discuss its appearance in rather distant research areas:
 values of quadratic forms (Perron Identity for Markov spectrum)
 the 2nd Kepler law on planetary motion
 Global relation on singularities of toric varieties 
03/12/2019 3:00 PMMathematics Building, Room: MB503Jan Sbierski (Oxford)Uniqueness & nonuniqueness results for wave equations
A wellknown theorem of ChoquetBruhat and Geroch states that for given smooth initial data for the Einstein equations there exists a unique maximal globally hyperbolic development. In particular, time evolution of globally hyperbolic solutions is unique. This talk investigates whether the same result holds for quasilinear wave equations defined on a fixed background. After recalling the notion of global hyperbolicity, we first present an example of a quasilinear wave equation for which unique time evolution in fact fails and contrast this with the Einstein equations. We then proceed by presenting conditions on quasilinear wave equations which ensure uniqueness. This talk is based on joint work with Harvey Reall and Felicity Eperon.

19/11/2019 3:00 PMMathematics Building, Room: MB503Giada Franz (ETH)Complexity criteria for free boundary minimal surfaces
Abstract
Given a threedimensional Riemannian manifold M with boundary, free
boundary minimal surfaces (FBMS) in M are critical points of the area
functional with respect to variations that constrain their boundary to
the boundary of M.
In recent years several different examples of FBMS have been discovered,
opening the problem of classifying the rich variety of all such surfaces
in a given ambient manifold.
Towards this purpose, we begin by studying how different properties of a
FBMS relate to each other. In particular we focus on the topology, the
area and the Morse index of a FBMS and we give a complete description of
the connections among these "complexity criteria".
This is joint work with Alessandro Carlotto. 
13/12/2019 10:00 AMMB503, Maths Building, QMUL Mile End CampusMiles Simon (Magdeburg) Natasa Sesum (Rutgers) Burhard Wilking (Münster)BrusselsLondon Geometry Seminar
TBA

26/11/2019 3:00 PMMathematics Building, Room: MB503Miklós Pálfia (Szeged)On the recent advances in the multivariable theory of operator means
The origins of this talk go back to the fundamental theorem of Loewner in 1934 on operator monotone real functions and also to
the hyperbolic geometry of positive matrices. Among others it lead to the KuboAndo theory of twovariable operator means
of positive operators in 1980. One of the nontrivial means of the KuboAndo theory is the noncommutative generalization of the
geometric mean which is intimately related to the hyperbolic, nonpositively curved Riemannian structure of positive matrices.
This geometry provides a key tool to define multivariable generalizations of twovariable operator means. Arguably the most important
example of them all is the Karcher mean which is the center of mass on this manifold. This formulation defines this mean
for probability meaures on the cone of positive definite matrices extending further the multivariable case. Even the infinite dimensional
case of positive operators is tractable by abandoning the Riemannian structure in favor of a BanachFinsler structure provided by
Thompson's part metric on the cone of positive definite operators. This metric enables us to develop a general theory of means of
probability measures defined as unique solutions of nonlinear operator equations on the cone, with the help of contractive semigroups
of nonlinear operators. 
21/11/2019 3:00 PMMathematics Building, Room: MB503Chris Bruce (University of Victoria)Semigroup C*algebras associated with arithmetic progressions
Congruence monoids in the ring of integers are given by certain unions of arithmetic progressions. To each congruence monoid, there is a canonical way to associate a semigroup C*algebra. I will explain this construction and then discuss joint work with Xin Li on Ktheoretic invariants. I will also briefly indicate how all of this generalizes to congruence monoids in the ring of integers of an arbitrary algebraic number field.
(Note the special time of the seminar.)

21/11/2019 12:00 PMMathematics Building, Room: MB503Kevin Brix (University of Copenhagen)Fine structure of C*algebras associated to topological dynamics
Symbolic dynamical systems have generated a wide a rich class of C*algebras with interesting properties. Recently, we have learned that these C*algebras remember a surprising amount of the information about the underlying dynamical system if we include the finer structure of the algebra as part of the data. This finer structure could be commutative subalgebras or certain circle actions. There will be an emphasis on open problems.
(Note the special time of the seminar.)

12/11/2019 3:00 PMMathematics Building, Room: MB503Katrin Leschke (Leicester)Title: Links between the integrable systems of a CMC surface
Abstract: A CMC surface in 3space is constrained Willmore and isothermic. It is well known that these 3 surface classes are each determined by a family of flat connections. In this talk we discuss links between the corresponding families of flat connections: we show that parallel sections of the associated family of flat connections of the harmonic Gauss map give algebraically the parallel sections of the other families. In particular, we obtain links between transformations of CMC surfaces, isothermic surfaces and constrained Willmore surfaces which are given by parallel sections, such as the associated family, the simple factor dressing and the Darboux transformation.

30/10/2019 3:30 PMRoom 516, G.O. Jones BuildingFelicity Eperon (Cambridge)Strong cosmic censorship in de Sitter spacetimes
There has been much interest in whether or not strong cosmic
censorship holds in de Sitter spacetimes. I will give an overview of
the strong cosmic censorship conjecture in general and more
specifically for ReissnerNordstromde Sitter and Kerrde Sitter black
holes. For Kerrde Sitter, I will explain how the quasinormal modes
can be used to show that strong cosmic censorship is indeed respected.(This seminar is held jointly with the Relativity and Cosmology Seminar)

22/10/2019 3:00 PMMathematics Building, Room: MB503Alessandro Pigati (ETH Zürich)Codimension two minmax minimal submanifolds from PDEs
Abstract: The AllenCahn functional provides a way to construct minmax minimal hypersurfaces, in an ambient closed Riemannian manifold, as limiting interfaces in a phase transition between two different states. A naive attempt to carry out a similar theory in codimension two would be to use the GinzburgLandau functional.
After briefly describing the difficulties arising with this functional, we will see how they disappear looking instead at the YangMillsHiggs action, whose features are strikingly similar to those of AllenCahn. We will also glimpse a minmax construction of codimension two minmax integer stationary varifolds using this approach. This is joint work with Daniel Stern (Princeton University  University of Toronto). 
05/11/2019 3:00 PMMathematics Building, Room: MB503Athanasios Chatzikaleas (Paris, UPMC)On blowup of corotational wave maps
We consider corotational wave maps from the (1 + d)dimensional Minkowski space into the dsphere for d ≥ 3 odd. This is an energysupercritical model which is known
to exhibit finitetime blowup via selfsimilar solutions. Based on a method developed by Donninger and Schörkhuber, we prove the asymptotic nonlinear stability of the
“groundstate” selfsimilar solution. 
15/10/2019 3:00 PMMathematics Building, Room: MB503Timothy Buttsworth (Cornell)Local stability of Einstein metrics under the Ricci iteration
Abstract:
A Ricci iteration is a sequence of Riemannian metrics on a manifold such that every metric
in the sequence is equal to the Ricci curvature of the next metric. These sequences of metrics
were introduced by Rubinstein to provide a discretisation of the Ricci flow. In this talk, I will
discuss the relationship between the Ricci iteration and the Ricci flow. I will also describe
a recent result concerning the existence and convergence of Ricci iterations close to certain
Einstein metrics. (Joint work with Max Hallgren) 
08/10/2019 3:00 PMMathematics Building, Room: MB503Mario Schulz (QMUL)Yamabe flow on noncompact manifolds
Abstract:
Yamabe flows are solutions to a geometric evolution equation which tends
to evolve a given Riemannian metric towards a conformal metric of
constant scalar curvature. On any closed Riemannian manifold the
existence and uniqueness of a Yamabe flow is known. The question of
wellposedness is more delicate if the initial manifold is noncompact
and uniqueness fails in general. We examine the existence and uniqueness
of instantaneously complete Yamabe flows starting from noncompact,
possibly incomplete Riemannian manifolds of arbitrary dimension. In this
context, we find a sharp condition on the dimension of a submanifold
which implies that its removability as a singularity is necessarily
preserved along the Yamabe flow. 
01/10/2019 3:00 PMMathematics Building, Room: MB503Iván Moyano (Nice)Spectral inequalities for the Schrödinger operator \Delta_x + V(x) in R^d
In this talk, we will first review some classical results on the socalled
’spectral inequalities’, which yield a sharp quantification of the unique
continuation of the spectral family associated with the LaplaceBeltrami
operator in a compact manifold. In a second part, we will discuss how to
obtain the spectral inequalities associated to the Schrodinger operator
$\Delta_x + V(x)$, in R^{d}, in any dimension $d \geq 1$, where
$V=V(x)$ is a real analytic potential. In particular, we can handle some long
range potentials. This is a joint work with Prof G. Lebeau (Université de
NiceCôte d'Azur, France). 
25/09/2019 3:30 PMRoom 516, G.O. Jones BuildingAlex Schenkel (Nottingham)Boundaries and edge modes in gauge theories
Abstract:
Recent studies of gauge and gravity theories on spacetimes with
boundaries revealed an interesting interplay between gauge symmetries
and boundaries. Quite surprisingly, one finds new physical degrees of
freedom, called edge modes, that live only on the boundary and play a
crucial role in physical applications such as entanglement entropy
calculations and topological insulators. In this talk, I will provide a
conceptual and mathematical interpretation of such edge mode phenomena
in terms of basic homological algebra and show that this naturally
explains the concrete models proposed by Donnelly and Freidel. This talk
is based on a joint work with P. Mathieu, N. Teh and L. Wells
[arXiv:1907.10651]. 
15/07/2019 3:00 PMG.O. Jones Building, Room 610Hanfeng Li (SUNY at Buffalo)Entropy and combinatorial independence
Topological entropy is a numerical invariant for group actions on compact spaces. Whether the entropy is positive or not makes a fundamental difference for the dynamical behavior. When a group G acts on a compact space X, a subset H of G is called an independence set for a finite family W of subsets of X if for any finite subset M of H and any map f from M to W, there is a point x of X with sx in f(s) for all s in M. I will discuss how positivity of entropy can be described in terms of density of independence sets, and give a few applications including the relation between positive entropy and LiYorke chaos. The talk is based on various joint works with David Kerr and Zheng Rong.

20/03/2019 3:30 PMG.O. Jones Building, Room 516Claude Warnick (Cambridge)Black holes and scattering resonances
Abstract: Recent experiments have, for the first time, directly measured gravitational waves created by colliding black holes. An important part of the signal from such events is the `ringdown’ phase where a distorted black hole emits radiation at certain fixed (complex) frequencies called the quasinormal frequencies. To mathematically model this phenomenon, one should study geometric wave equations on a class of open geometries. I will discuss how the quasinormal frequencies can be realised as eigenvalues of a (nonstandard) spectral problem, with connections to scattering resonances on asymptotically hyperbolic manifolds. If time permits I will also discuss recent work with Gajic on the asymptotically flat case.

05/03/2019 3:00 PMRoom W316, Queens' BuildingCANCELLED  Katrin Leschke (Leicester)CANCELLEDMinimal surfaces via Quaternionic Holomorphic GeometryAbstract: In this talk, I shall explain how a generalisation of holomorphic curves in complex projective space to quaternionic holomorphic curves can be used to study conformal immersions, and in particular minimal surfaces, in 3space.As an application we will discuss the Simple Factor Dressing and the Darboux transformation of minimal surfaces.

26/03/2019 3:00 PMRoom W316, Queens' BuildingStephen McCormick (Uppsala)Title: Some recent developments on Bartnik's quasilocal mass
Abstract: The problem of quasilocal mass in general relativity is the problem of assigning some meaningful notion of the total mass (or energy) contained in a bounded domain. We first will give an introduction to the problem and review several important proposed definitions of quasilocal mass, before turning to discuss some recent progress on understanding the definition due to Bartnik. We will discuss a method to obtain estimates of the Bartnik mass in the CMC case, and briefly mention how these estimates can be used to obtain estimates outside of the CMC case. If time permits we will then present a new formula for the evolution of the full spacetime Bartnik mass, under some strict assumptions. The work presented here include results obtained in collaboration with Armando Cabrera Pacheco, Carla Cederbaum, and Pengzi Miao.

20/02/2019 3:30 PMG.O. Jones Building, Room 516Maximilian Attems (University of Santiago de Compostela)Shockwave collisions across a phase transitionEver since the discovery of the quarkgluon plasma (QGP) the location
of the critical point in the QCD phase diagram  the end point of
the firstorder transition between hadron matter and QGP  has been
a main research goal for heavyion collision experiments. We use the
gauge/gravity duality to study as first a fourdimensional, strongly
coupled gauge theory with a firstorder thermal phase transition.
In the dual gauge theory we calculate the evolution and saturation
of the spinodal instability. We uncover a new surprising example
of the applicability of hydrodynamics to systems with large gradients.
We discover with shockwave collisions that in theories with a first
order phase transition, a longlived, quasistatic state may be formed.
Moreover, we show the MuellerIsraelStewarttype formulation of
hydrodynamics to fail to describe pressures near a critical point.(This seminar is held jointly with the Relativity and Cosmology Seminar)

12/02/2019 3:00 PMRoom W316, Queens' BuildingMariel Saez (Pontificia Universidad Católica de Chile)On the uniqueness of graphical mean curvature flow
Abstract: In this talk I will discuss recent work with P. Daskalopoulos on sufficient conditions to prove uniqueness of complete graphs evolving by mean curvature flow. It is interesting to remark that the behaviour of solutions to mean curvature flow differs from the heat equation, where nonuniqueness may occur even for smooth initial conditions if the behaviour at infinity is not prescribed for all times.

05/02/2019 3:00 PMRoom W316, Queens' BuildingAndrea Mondino (Warwick)Some smooth applications of nonsmooth Ricci curvature lower bounds
Abstract:
I will discuss some applications to smooth Riemannian manifolds of the optimal transport formulation of Ricci curvature lower bounds, leading to the theory of possibly nonsmooth CD spaces by LottSturmVillani.These include: rigidity/stability of the LevyGromov inequality and an
almost euclidean isoperimetric inequality motivated by the celebrated
Perelman's PseudoLocality Theorem for Ricci flow. (joint work with Fabio Cavalletti, SISSA). 
12/03/2019 3:00 PMRoom W316, Queens' BuildingZoe Wyatt (Edinburgh)Attractors of the EinsteinKleinGordon system
A key question in general relativity is whether solutions to the Einstein equations, viewed as an initial value problem, are stable to small perturbations of the initial data. For example, previous results have shown that the Milne spacetime, which represents an expanding universe emanating from a big bang singularity with a linear scale factor, is a stable solution to the Einstein equations. With such a slow expansion rate, particularly compared to related isotropically expanding models (such as the exponentially expanding de Sitter spacetime observed in our universe), there are interesting questions one can ask about stability of this spacetime. Previous results have shown that the Milne model is a stable solution to the vacuum Einstein, EinsteinKleinGordon and EinsteinVlasov systems. Motivated by techniques from the last result, I will present a new proof of the stability of the Milne model to the EinsteinKleinGordon system and compare our method to a recent result of J. Wang. This is joint work with D. Fajman.

22/01/2019 3:00 PMRoom W316, Queens' BuildingAndrew McCleod (UCL)Global Regularity of ThreeDimensional Ricci Limit Spaces
In joint work with Peter Topping we introduce local pyramid Ricci flows, existing on uniform regions of spacetime, that are inspired by Hochards partial Ricci flows. As an application of pyramid Ricci flows, we construct a global homeomorphism from any 3D Ricci limit space to a smooth manifold that is biHolder once restricted to any compact subset. This extends the recent work of Miles Simon and Peter Topping, and builds upon their techniques.

26/02/2019 3:00 PMRoom W316, Queens' BuildingLéo Bigorgne (Orsay)Asymptotics properties of the small data solutions of the VlasovMaxwell system
The VlasovMaxwell system is a classical model in plasma physics. Glassey and Strauss proved global existence for the small data solutions of this system under a compact support assumption on the initial data. I will present how vector field methods can be applied to revisit this problem. In particular, it allows to remove all compact support assumptions on the initial data and obtain sharp asymptotics on the solutions. We will also discuss the null structure of the system which constitutes a crucial element of the proof.

19/02/2019 11:30 AMUniversity College London11:30 Giovanni Catino (Milano) 14:00 Gilles Caron (Nantes) 15:30 Yuxin Ge (Toulouse)BRUSSELSLONDON XVII : Conformal geometry
11:30 Giovanni Cation (Milano)  TBA
14:00 Gilles Caron (Nantes)  TBA
15:30 Yuxin Ge (Toulouse)  TBAThe first talk will take place in Room 505 of the mathematics department at University College London. The lunch and subsequent talks will take place in Room 106 in Gordon House. Early arrivals will be met with coffee and cakes in Room 502 of the mathematics department and lunch will be held at 12.30, between the first and second talks.
Registration is free, but necessary so that we know how many people to expect. To register please visit http://geometry.ulb.ac.be/brusselslondon/. Lunch will be provided for all registered attendees.
Further details (including maps indicating the location of the rooms) will be available on the seminar website: http://geometry.ulb.ac.be/brusselslondon/ 
30/01/2019 3:30 PMG.O. Jones Building, Room 516Mahdi Godazgar (QMUL)Asymptotic charges in gravityI will give an overview of my recent research on the definition of asymptotic charges in asymptotically flat spacetimes, including the definition of subleading BMS charges and the relation to the conserved NewmanPenrose charges at null infinity.
(This seminar is held jointly with the Relativity and Cosmology Seminar)

15/01/2019 3:00 PMRoom W316, Queens' BuildingMatthieu Léautaud (École Polytechnique)Unique continuation and intensity of waves in the shadow region
We are interested in the following unique continuation question: does the intensity of waves observed from a subdomain during a time interval determine their total energy? What is the intensity of waves in the shadow of an obstacle? In this talk, we shall give a stability estimate answering to these questions in a quantitative way.
This is joint work with Camille Laurent.

14/12/2018 3:00 PMQueens' Building, Room: W316Reza Pakzad (University of Pittsburgh)Regularity dependent anomalous solutions in select PDEs
Abstract: We will discuss the qualitative change of behavior for solutions to certain classes on PDEs in various Holder and Sobolev regularity regimes, with a focus on the MongeAmpere equations. We will discuss various techniques, from theory of mappings with finite distortion and geometric measure theory to convex integration, which are used to obtain a panorama of yet incomplete results.

28/11/2018 3:30 PMG.O. Jones Building, Room: 516Haris Markakis (UIUC/QMUL)Stability of iterative algorithms for elliptic equations in Newtonian gravity and general relativity
Similar methods have been used to construct models of rapidly rotating or binary stars, in Newtonian and relativistic contexts. The choice of method has been based on numerical experiments, which indicate that particular methods converge quickly to a solution, while others diverge. The theory underlying these differences, however, has not been understood. In an attempt to provide a better theoretical understanding, we analytically examine the behavior of different iterative schemes near an exact static solution. We find the spectrum of the linearized iteration operator and show for selfconsistent field methods that iterative instability corresponds to unstable modes of this operator. Minimizing the maximum eigenvalue accelerates convergence and allows computation of highly compact configurations that were previously inaccessible via selfconsistent field methods.
(This seminar is held jointly with the Relativity and Cosmology Seminar)

20/11/2018 3:00 PMQueens' Building, Room: W316Ali Feizmohammadi (UCL)Uniqueness of a potential from boundary data in locally Euclidean geometries
In the first part of the talk we will give an overview of the inverse problem of recovering an unknown coefficient for an ellipitic PDE from boundary measurements. In particular we will derive a uniqueness result for determining a potential function for the Schrodinger operator in a Riemannian manifold from the knowledge of the local Dirichlet to Neumann map using the machinery of complex geometric optics and Carleman estimates. In the second part of the talk we will discuss a hyperbolic analogue of the same inverse problem.

05/11/2018 11:00 AMQueens' Building, W316Maxim Olchanyi, Department of Physics, University of Massachusetts, BostonPhysicists's tricks played with PDEs: dimensional analysis, orderofmagnitude estimates, etc.
Abstract: I will test drive some ideas, expanded in the PDE direction, from the second edition of 'BackOfTheEnvelope Quantum Mechanics: With Extensions To ManyBody Systems And Integrable PDEs.’ The talk will be accessible to researchers and postgraduates in both mathematics and physics.

06/11/2018 3:00 PMRoom W316, Queens' BuildingBruno Vergara (ICMAT)Convexity of Whitham's highest cusped wave
In this talk I will discuss a conjecture of Ehrnström and Wahlén on the profile of travelling wave solutions of extreme form to Whitham's nonlocal dispersive equation. We will see that there exists a highest, cusped and periodic solution that is convex between consecutive crests, at which C^{1/2}regularity has been shown to be optimal. The talk is based on joint work with A. Enciso and J. GómezSerrano.

13/11/2018 3:00 PMRoom W316, Queens' BuildingAlberto Enciso (ICMAT)The evolution of some geometric structures under the Euler and NavierStokes equations
In this talk we will be interested in the evolution under the Euler and NavierStokes equations of several geometric structures defined by the vorticity of the fluid. First we will see how vortex lines and vortex tubes of complicated topologies are created and destroyed in the 3D NavierStokes equations. Next we will consider the emergence of nonsmooth interfaces of surprising geometry in the free boundary Euler equations. The talk is based on joint work with D. Córdoba, C. Fefferman, N. Grubic, R. Lucà and D. PeraltaSalas.

23/10/2018 3:00 PMRoom W316, Queens' BuildingJarrod Williams (QMUL)The Friedrich–Butscher method for the construction of initial data in General Relativity
The construction of initial data for the Cauchy problem in General Relativity is an interesting problem from both the mathematical and phys ical points of view. As such, there have been numerous methods studied in the literature —the “Conformal Method” of Lichnerowicz–Choquet Bruhat–York and the “gluing” method of Corvino–Schoen being perhaps the bestexplored. In this talk I will describe an alternative, perturbative, approach proposed by A. Butscher and H. Friedrich, and show how it can be used to construct nonlinear perturbations of initial data for spatially closed analogues of the “k = −1” FLRW spacetime. Time permitting, I will discuss possible refinements/extensions of the method, along with its generalisation to the full Conformal Constraint Equations of H. Friedrich.

09/10/2018 1:00 PMRoom W316, Queens' BuildingBen Lambert  UCLHigher codimensional spacelike mean curvature flow and applications NOTE!Special time
Abstract : We consider entire higher codimensional mean curvature flow in $R^{n,m}$ of $n$dimensional spacelike manifolds and prove a long time existence theorem starting from arbitrary spacelike initial data. We will see that the key to the proof is to demonstrate local spacelike gradient estimates, and to get around difficulties with cutoff functions in $R^{n,m}$. Surprisingly, this theorem leads to some new long time existence results for the $G_2$Laplacian flow.

29/05/2018 3:00 PMRoom W316, Queens' BuildingHuaxin Lin (University of Oregon)Classification of separable simple stably projectionless C*algebras
We will present a classification theorem for amenable simple stably projectionless C*algebras with generalized tracial rank one.
With many decades' work, unital separable simple amenable Zstable C*algebras in the UCT class have been classified by the Elliott invariant. Nonunital case can be easily reduced to the unital case if the stabilized C*algebras have a nonzero projection.
However, there are many nonunital separable simple amenable C*algebras which are stably projectionless. In other words, K_0(A)_+ = {0}.
One of these simple C*algebras is what we called Z_0. This C*algebra can be constructed as an inductive limit of socalled noncommutative finite CW complexes. It has exactly one tracial state and has the properties that K_0(Z_0) = Z, K_0(Z_0)_+ = {0} and K_1(Z_0) = {0}.
We will show that there is exactly one Z_0 in the class of simple separable C*algebras with finite nuclear dimension and satisfying the UCT (up to isomorphism).
Let A and B be two separable simple C*algebras satisfying the UCT and have finite nuclear dimension.
We show that A \otimes Z_0 \cong B \otimes Z_0 if and only if Ell(B \otimes Z_0) = Ell(A \otimes Z_0).
A class of simple separable C*algebras which are approximately subhomogeneous whose spectra having bounded dimension is shown to exhaust all possible Elliott invariant for C*algebras of the form A \otimes Z_0, where A is any finite separable simple amenable C*algebra.
Suppose that A and B are two finite separable simple C*algebras with finite nuclear dimension satisfying the UCT such that both K_0(A) and K_0(B) are torsion (but arbitrary K_1).
One consequence of the main results in this situation is that A \cong B if and only if A and B have isomorphic Elliott invariants. 
16/10/2018 3:00 PMRoom W316, Queens' BuildingTakuya Takeishi (Kyoto Institute of Technology)Reconstructing the BostConnes semigroup actions from Ktheory
In this talk, we give a result of the complete classification of BostConnes systems. For a number field K, there is a semigroup dynamical system attached to K, which is so called the BostConnes semigroup dynamical systems. By taking the crossed product, we obtain the BostConnes C*algebra for K. We show that BostConnes C*algebras for two number fields are isomorphic if and only if the BostConnes semigroup actions are conjugate. Together with the reconstruction results in number theory by Cornelissende SmitLiMarcolliSmit, we conclude that two BostConnes C*algebras are isomorphic if and only if the original number fields are isomorphic.

02/10/2018 3:00 PMRoom W316, Queens' BuildingKevin Hughes (Bristol)L^p improving inequalities and sparse bounds for discrete averages
We will introduce L^p improving inequalities for discrete spherical averages and their generalizations. Subsequently we will give a new proof of a recent theorem of Kesler on sparse bounds for such averages. The latter is joint with Tess Anderson. Throughout we will pay attention to motivation and discuss a couple principles that influence the area.

26/09/2018 3:30 PMG.O. Jones Building, Room 516Thomas Johnson (University of Cambridge)The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge
(This seminar is held jointly with the Relativity and Cosmology Seminar)
In this talk we shall discuss our recent work which establishes that the Schwarzschild family of black holes are linearly stable as a family of solutions to the Einstein vacuum equations when expressed in a generalised wave gauge. The result therefore provides an important step towards a resolution of the black hole stability problem in general relativity and thus complements the recent work of Dafermos—Holzegel—Rodnianski in a similar vein as to how the work of Lindblad—Rodnianski complemented that of Christodoulou—Klainerman in establishing the nonlinear stability of the Minkowski space.

30/10/2018 9:00 AMTBA(Twoday conference)Geometric Analysis Days: Intersections of Geometric Analysis and Mathematical Relativity
This is a twoday miniconference on geometric analysis and mathematical relativity. See here for details.

03/04/2018 3:00 PMRoom W316, Queens' BuildingShadi TahvildarZadeh (Rutgers University)Riesz, HarishChandra, and the Quest for a Quantum Theory of Light
In this talk I explain how my colleague Michael Kiessling and I used the groundbreaking work of Marcel Riesz on the analysis of Cliffordalgebravalued wave equations, and combined it with a key observation of HarishChandra made while he was Dirac's student in Cambridge to obtain a relativistic quantummechanical wave equation for a photon (the quantum of light) in positionspace representation, a task that has been declared "impossible" by many prominent physicists. I will also show that this wave equation has all the properties needed in order to treat the photon just like an electron, i.e., a pointparticle whose motion is guided by a wave function defined on its configuration space. As an application, I will present some recent results we have, in collaboration with Matthias Lienert, concerning a fullyrelativistic, twobody photonelectron system in one space dimension, thereby paving the way for a rigorous geometric study of quantum effects in the interactions of radiation with matter.

27/03/2018 3:00 PMAli Feizmohammadi (UCL)(Cancelled)

24/04/2018 3:00 PMRoom W316, Queens' BuildingBaptiste Morisse (Cardiff)Wellposedness of weakly hyperbolic systems of PDEs in Gevrey regularity
I consider systems of firstorder PDEs, which are weakly hyperbolic: the spectrum of the principal symbol is real but eigenvalues may cross. Close to one of those crossing eigenvalues, lower order linear terms may induce a typical Gevrey growth in frequency. I will present an energy estimate in Gevrey regularity, using an approximate symmetrizer of the principal symbol. The symbol of such an approximate symmetrizer is in a special class of symbols, related to a specific metric in phase space. For such symbols, composition of associated operators lead to error terms that only can be handle thanks to the Gevrey energy.

17/04/2018 3:00 PMRoom W316, Queens' BuildingCécile Huneau (École Polytechnique)TBA

13/03/2018 3:00 PMRoom W316, Queens' BuildingSuresh Eswarathasan (Cardiff)$L^p$ restriction of eigenfunctions to random Cantortype sets
Let $(M,g)$ be a compact Riemannian surface without boundary. Consider the corresponding $L^2$normalized LaplaceBeltrami eigenfunctions. Eigenfunctions of this type arise in physics as modes of periodic vibration of drums and membranes. They also represent stationary states of a free quantum particle on a Riemannian manifold. In the first part of the lecture, I will give a survey of results which demonstrate how the geometry of $M$ affects the behaviour of these special functions, particularly their “size” which can be quantified by estimating $L^p$ norms.
In joint work with Malabika Pramanik (U. British Columbia), I will present in the second part of my lecture a result on the $L^p$ restriction of these eigenfunctions to random Cantortype subsets of $M$. This, in some sense, is complementary to the smooth submanifold $L^p$ restriction results of BurqGérardTzetkov ’06 (and later work of other authors). Our method includes concentration inequalities from probability theory in addition to the analysis of singular Fourier integral operators on fractals. 
20/03/2018 10:00 AMUniversity College LondonCarla Cederbaum (Tübingen), Piotr Chrusciel (Vienna), Mihalis Dafermos (Cambridge, Princeton)BrusselsLondon Geometry Seminar XIII: General Relativity (External)
See http://geometry.ulb.ac.be/brusselslondon/ for additional details.

13/02/2018 3:00 PMRoom W316, Queens' BuildingDavid Kerr (Texas A&M University)Entropy and bounded orbit equivalence
Recently Austin showed that, for free probabilitymeasurepreserving actions of
countable infinite amenable groups, entropy is preserved under bounded and L^1
orbit equivalence, and more generally that an entropy scaling formula holds
for stable versions of these equivalences. I will explain how Austin's approach
translates into the realm of topological dynamics and then speculate on how it
might extend beyond the amenable setting. 
27/02/2018 3:00 PMRoom W316, Queens' BuildingMatthias Wink (Oxford)Constructions of Ricci Solitons
All known singularity models in Ricci flow are Ricci solitons. In this talk we will construct new steady and expanding Ricci solitons of cohomogeneity one. The solitons are defined on complex line bundles over products of Fano manifolds or HP^{m} \setminus \{ point \} amongst others. The main tool is a general estimate on the growth of the soliton potential.

30/01/2018 3:00 PMRoom W316, Queens' BuildingLothar Schiemanowski (Kiel)A blowup criterium for the spinor flow on surfaces
The spinorial energy functional is a functional on the space of metrics whose critical points are special holonomy metrics in dimension 3 and higher. The spinor flow is its gradient flow. On surfaces the functional has a different geometric interpretation which will be explained in the talk. After that I will report on recent work concerning the formation of singularities, based on a decomposition of the flow into the evolution of a conformal factor and a movement of constant curvature metrics, which has been introduced by Buzano and Rupflin for the Ricciharmonic flow.

06/02/2018 3:00 PMRoom W316, Queens' BuildingLaurent Mazet (Laboratoire d'Analyse et Mathématiques Appliquées, Université ParisEst)Characterization of $f$extremal disks
A $f$extremal domain in a manifold $M$ is a domain $\Omega$ which admits a positive solution $u$ to the equation $\Delta u+f(u)=0$ with $0$ Dirichlet boundary data and constant Neuman boundary data. Thanks to a result of Serrin, it is known that in $\mathbb R^n$ such a $f$extremal domain has to be a round ball. In this talk, we will prove that a $f$extremal domain in $\mathbb S^2$ which is a topological disk is a geodesic disk under some asumption on $f$. This is a joint work with J.M. Espinar.

16/01/2018 3:00 PMRoom W316, Queens' BuildingDavid Hilditch (IST Lisbon)TBA

06/12/2017 4:00 PMW316Luc Nguyen (Oxford)Existence and uniqueness of Green's function to a nonlinear Yamabe problem
For a given finite subset $S$ of a compact Riemannian manifold $(M,g)$ whose Schouten curvature tensor belongs to a given cone, we prove the existence and uniqueness of a conformal metric on $M \setminus S$ such that each point of $S$ corresponds to an asymptotically flat end and that the Schouten tensor of the new conformal metric belongs to the boundary of the given cone. Joint work with Yanyan Li.

28/11/2017 12:45 PM12th BrusselsLondon geometry seminar at Université libre de Bruxelles

21/11/2017 3:00 PMW316Davoud Cheraghi (Imperial College London)Topological branched coverings and invariant complex structures
Let f be an orientation preserving branched covering of the two dimensional sphere. Is f realized (up to homotopy) by a rational function of the sphere? If yes, is the corresponding rational function unique up to the Mobius transformations (the rigidity)? These questions amount to the existence and uniqueness of a complex structure that is invariant under the action of (the homotopy class of) f. The geometric and topological structure of "the orbits of the branched points”, play a key role in these problems. When this set has finite cardinality, a classical result of W. Thurston provides a complete topological characterisation of the branched coverings that are realised by rational functions (and the uniqueness). On the other hand, when the orbits of branched points forms a more complicated set of points, say a Cantor set, the questions have been extensively studied over the last three decades. In this talk we survey the main results of these studies, and describe a recent advance made on the uniqueness part using a renormalization technique.

14/11/2017 3:00 PMW316Lucas AmbrozioFree boundary minimal hypersurfaces
When a minimal submanifold with boundary on a given Riemannian manifold meets another hypersurface orthogonally, it is said to be a free boundary minimal submanifold. This constraint is very natural from a variational point of view. We will talk about some recent progress on the understanding of compact free boundary minimal hypersurfaces in various ambient domains. In particular, we will discuss our work on classification of free boundary minimal surfaces in the unit ball of the Euclidean space (joint with I Nunes, UFMA), on some general index estimates, and on convergence of sequences of free boundary minimal hypersurfaces under various assumptions (joint with A. Carlotto, ETH, and B. Sharp, Warwick).

07/11/2017 3:00 PMW316Thomas Bäckdahl (Albert Einstein Institute)Symmetries and conservation laws for linearized gravity
In this talk I will review recent results on the structure of the linearized gravity equations. The results apply to yield new symmetry operators and conservation laws for linearized gravity on the Kerr spacetime, as well as new hyperbolic systems governing the linearized gravitational field.

25/10/2016 3:00 PMMaths 203Arick Shao (QMUL)Uniqueness Theorems on Asymptotically Antide Sitter Spacetimes
In theoretical physics, it is often conjectured that a correspondence exists between the gravitational dynamics of asymptotically Antide Sitter (AdS) spacetimes and a conformal field theory of their boundaries. In the context of classical relativity, one can attempt to rigorously formulate a correspondence statement as a unique continuation problem for PDEs: Is an asymptotically AdS solution of the Einstein equations uniquely determined by its data on its conformal boundary at infinity?
In this presentation, we establish a key step in toward a positive result; we prove an analogous unique continuation result for linear and nonlinear wave equations on fixed asymptotically AdS spacetimes satisfying a positivity condition at infinity. We show, roughly, that if a wave ϕ on this spacetime vanishes on a sufficiently large but finite portion of its conformal boundary, then ϕ must also vanish in a neighbourhood of the boundary. In particular, we highlight the analytic and geometric features of AdS spacetimes which enable this uniqueness result, as well as obstacles preventing such a result from holding in other cases.
This is joint work with Gustav Holzegel.

01/03/2016 3:00 PMM103Carlos Siqueira (Imperial College London)Hausdorff dimension of solenoidal Julia sets
Using the technique of holomorphic motions, we study the regularity of the limit set of the oneparameter family of holomorphic correspondences (wc)^q=z^p, outlining some of the main contributions in the field in the last decades. This family is the simplest generalisation of the quadratic family z^2+c. In the quasi postcritically finite case, the limit set splits into a repeller and an attractor: the usual Julia set (closure of repelling periodic points) and the dual Julia set (closure of attracting periodic points). Conformal iterated function systems hidden in the dynamics of this correspondence appear naturally in the form of dual Julia sets. We also estimate the Hausdorff dimension of the Julia set using the formalism of Gibbs states.

28/10/2014 3:00 PMM103Shur multipliers and closability properties
Schur multipliers were introduced by Schur in early 20th century and have since
then found a considerable number of applications in Analysis and enjoyed an intensive
development. Apart from the beauty of the subject itself, sources of interest in them
were connections with Perturbation Theory, Harmonic Analysis, the Theory of Opera
tor Integrals and other. Schur multipliers have a simple definition: a bounded function
φ : N x N > C (where N and C are the set of positive integers and complex numbers
respectively) is called a Schur multiplier if whenever a matrix (aij) gives rise to
a (bounded) transformation Sφ of the space $l_2$, the matrix (φ(i, j)aij) does so as
well. A characterisation of Schur multipliers was given by Grothendieck in his Resume.
If instead of $l_2$ we consider a pair of Hilbert spaces H1 = L2(X, μ), H2 = L2(Y, ν)
then there is also a method (due mainly to Birman and Solomyak) to relate to some
bounded functions φ on X x Y linear transformations Sφ on the space B(H1,H2) (these
transformations are called masurable Schur multipliers or, in a more general setting of
spectral measures μ, ν, double operator integrals). Namely one defines firstly a map Sφ
on Hilbert Schmidt operators multiplying their integral kernels by φ; if this map turns
out to be bounded in operator norm, extend it to the space K(H1,H2) of all compact
operators by continuity. Then Sφ is defined on B(H1,H2) as the second adjoint of
the constructed map of K(H1,H2). A characterisation of all such multipliers was first
established by Peller: Schur multipliers are percisely the functions of the formφ(x, y) =Σ a_k(x)b_k(y)
such that (esssup Σa_k(x)^2)(esssup Σb_k(x)^2) < \infty.
We shall discuss results on Schur multipliers and the question for which φ the map
Sφ is closable in the operator norm or in the weak* topology of B(H1,H2). If φ is of
Toeplitz type, i.e. φ(x, y) = f(x  y) ( x, y in G), where G is a locally compact abelian
group then the question is related to certain questions about the Fourier algebra A(G);
if φ(x, y) is of the form (f(x)f(y))/(xy) then the property is related to "operator
smoothness" of f. This is a joint work with V.Shulman and I.Todorov.
1 
06/12/2017 4:00 PMW316Luc Nguyen (Oxford)TBA

31/10/2017 3:00 PMW316Andrew Morris (University of Birmingham)The method of layer potentials in $L^p$ and endpoint spaces for elliptic operators with $L^\infty$ coefficients
Abstract: We consider layer potentials for secondorder divergence form elliptic operators with bounded measurable coefficients on Lipschitz domains. A ''CalderónZygmund" theory is developed for the boundedness of the layer potentials under the assumption that null solutions satisfy interior de GiorgiNashMoser type estimates. In particular, we prove that $L^2$estimates for layer potentials imply sharp $L^p$ and endpoint space estimates. The method of layer potentials is then used to obtain solvability of boundary value problems. This is joint work with Steve Hofmann and Marius Mitrea.

03/10/2017 3:00 PMW316Juan Valiente Kroon (QMUL)Nonpeeling spacetimes
In this talk I will give an overview of Friedrich’s construction of a regular asymptotic initial value problem at spatial
infinity and the open questions related to it. In particular, I will show how this framework can be used to identify initial data sets for the vacuum Einstein field equations which should lead to spacetimes not satisfying the peeling behaviour. This is research in collaboration with Edgar Gasperin. 
26/09/2017 3:00 PMW316Grigorios Fournodavlos (University of Cambridge)Dynamics of the Einstein vacuum equations in the interior of a Schwarzschild black hole
We will discuss stability issues of a Schwarzschild singularity. I will describe past and recent work on the backward and forward initial value problem for the Einstein vacuum equations with near Schwarzschild configurations close to the singularity.

31/05/2017 3:30 PMPP1Peter Topping (Warwick)Mollification via Ricci flow
This is a talk of the BrusselsLondon Geometry seminar. For more information on this event, please visit the website at http://geometry.ulb.ac.be/brusselslondon/(link is external) .

31/05/2017 2:00 PMPP1Gerhard Huisken (Tübingen)Mean curvature flow in asymptotically flat 3manifolds and its applications
This is a talk of the BrusselsLondon Geometry seminar. For more information on this event, please visit the website at http://geometry.ulb.ac.be/brusselslondon/(link is external) .

31/01/2017 11:30 AMPP1Paul Feehan (Rutgers)Lojasiewicz inequalities for YangMills and harmonic map energy functions
This is a talk of the BrusselsLondon Geometry seminar. For more information on this event, please visit the website at http://geometry.ulb.ac.be/brusselslondon/(link is external) .

03/04/2017 4:45 PMPP1Huy Nguyen (QMUL)A ChernGaussBonnet formula for singular conformally flat evendimensional manifolds
This talk is part of the QMUL Geometric Analysis Day. For more information and to register, please visit the event website at http://www.maths.qmul.ac.uk/~buzano/geometricanalysis.html

03/04/2017 2:15 PMPP1Tobias Lamm (Karlsruhe)Limits of alphaharmonic maps
This talk is part of the QMUL Geometric Analysis Day. For more information and to register, please visit the event website at http://www.maths.qmul.ac.uk/~buzano/geometricanalysis.html

03/04/2017 2:55 PMPP1Barbara Nelli (L'Aquila)Minimal Surfaces in the Heisenberg Space
This talk is part of the QMUL Geometric Analysis Day. For more information and to register, please visit the event website at http://www.maths.qmul.ac.uk/~buzano/geometricanalysis.html

03/04/2017 10:30 AMPP1Gerard Besson (Grenoble)The space of complete metric of uniformly positive scalar curvature on open 3manifolds
This talk is part of the QMUL Geometric Analysis Day. For more information and to register, please visit the event website at http://www.maths.qmul.ac.uk/~buzano/geometricanalysis.html

14/03/2017 3:00 PMQueens Building W316Lauri Oksanen (UCL)Inverse boundary value problem for the wave equation
We consider the inverse boundary value problem for the wave equation in a geometric setting. This problem gives, for example, an idealized model of seismic imaging when the speed of sound is anisotropic but timeindependent. We present two recent results: one related to the case where the speed of sound is timedependent (joint work with Y. Kian, arXiv:1606.07243) and the other to the case where the wave equation is vector valued (joint work with Y. Kurylev and G. Paternain, arXiv:1509.02645).

08/03/2017 3:00 PMQueens Building W316Mahir Hadzic (KCL)Expanding large global solutions of the equations of compressible fluid mechanics
In a recent work Sideris constructed a finiteparameter family of compactly supported affine solutions to the free boundary isentropic compressible Euler equations satisfying the physical vacuum condition. The support of these solutions expands at a linear rate in time. We show that if the adiabatic exponent gamma belongs to the interval (1, 5/3] then these affine motions are nonlinearly stable; small perturbations lead to globalintime solutions that remain "close" to the moduli space of affine solutions and no shocks are formed in the process. Our strategy relies on two key ingredients: a new interpretation of the affine motions using an (almost) invariant action of GL(3) on the compressible Euler system and the use of Lagrangian coordinates. The former suggests a particular rescaling of time and a change of variables that elucidates a stabilisation mechanism, while the latter requires new ideas with respect to the existing wellposedness theory for vacuum free boundary fluid equations. This is joint work with Juhi Jang (USC).

07/03/2017 3:00 PMQueens Building W316Philippe G. LeFloch (Paris)The nonlinear stability of Minkowski spacetime for selfgravitating massive fields
I will discuss the global evolution problem for selfgravitating massive matter in the context of Einstein's theory and, more generally, of the f(R)theory of gravity. In collaboration with Yue Ma (Xian), I have investigated the global existence problem for the EinsteinKleinGordon system and established that Minkowski spacetime is globally nonlinearly stable in presence of massive fields. The original method proposed by Christodoulou and Klainerman as well as the proof in wave gauge by Lindblad and Rodnianski cover vacuum spacetimes or massless fields only. Analyzing the time decay of massive waves requires a completely new approach, the Hyperboloidal Foliation Method, which is based on a foliation by asymptotically hyperboloidal hypersurfaces and on investigating the algebraic structure of the EinsteinKleinGordon system.

28/02/2017 3:00 PMQueens Building W316Mat Langford (Berlin)Sharp onesided curvature estimates in mean curvature flow
We will present a sharp onesided curvature estimate for the mean curvature flow and some applications, in particular to ancient solutions of the flow.

14/02/2017 3:00 PMMaths 203Sylvain Maillot (Montpellier)Structure theory of open graph 3manifolds
Motivated by Gromov’s minimal volume problem, we introduce the class of noncompact graph 3manifolds. We show that some of the structure theory of compact graph manifolds, due to Waldhausen in the late 60s, goes through. However, some results do not; we will present examples to that effect.
Part of this is still work in progress.

07/02/2017 3:00 PMMaths 203Ben Sharp (Warwick)Estimates on the first Betti number of closed and freeboundary minimal hypersurfaces in positively curved manifolds
We will present some recent results which relate the Morse index of a minimal hypersurface with its first Betti number. The Morse index of a minimal hypersurface measures the number of different ways in which one can reduce area (up to second order). In the presence of positive curvature it is expected that the index controls the topology of such objects. We will state and prove some special cases of this phenomenon, in particular we show that in a variety of cases the first Betti number is linearly bounded from above by the index. In particular we will present separate joint works with Reto Buzano, Alessandro Carlotto and Lucas Ambrozio.

31/01/2017 3:00 PMMaths 203Carlo Mantegazza (Napoli)Evolution of planar networks of curves with multiple junctions
I will present the problem of the motion by curvature of a network of curves in the plane and I will discuss the stateoftheart of the subject, in particular, about existence, uniqueness, singularity formation and asymptotic behavior of the flow.

24/01/2017 3:00 PMMaths 203Takuya Takeishi (Kyoto)On the classification of BostConnes C*algebras
BostConnes C*algebra is a C*algebra attached to number fields. In my series of work, BostConnes C*algebras are shown to remember some number theoretic invariants. The next step we are interested in is to reconstruct C*algebraic structures from invariants. We are conjecturing that all information is concentrated on Kgroups of simple composition factors. Toward this, we are at first trying to give an isomorphism between BostConnes C*algebras after trivializing Ktheory. We give a partial result on this direction and explain what the remaining problem is.
This work is in progress. This is a joint work with Y. Kubota at the Univ. of Tokyo. 
17/01/2017 3:00 PMMaths 203Dominic Dold (Cambridge)Exponentially growing mode solutions to the KleinGordon equation in KerrAdS spacetimes
We consider solutions to the KleinGordon equation in the black hole exterior of KerrAdS spacetimes. It is known that, if the spacetime parameters satisfy the HawkingReall bound, solutions (with Dirichlet boundary conditions at infinity) decay logarithmically. We shall present our recent result of the existence of exponentially growing mode solutions in the parameter range where the HawkingReall bound is violated. We will discuss both Dirichlet and Neumann boundary conditions.

10/01/2017 3:10 PMMaths 203Chris PenroseMinimal Visibility in the Mandelbrot set

13/12/2016 3:00 PMMaths 203Mike Whittaker (Glasgow)Fractal substitution tilings and applications to noncommutative geometry
Starting with a substitution tiling, such as the Penrose tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles typically have fractal boundary. As an application of fractal tilings, we construct an odd spectral triple on a C*algebra associated with an aperiodic substitution tiling. Even though spectral triples on substitution tilings have been extremely well studied in the last 25 years, our construction produces the first truly noncommutative spectral triple associated with a tiling. My work on fractal substitution tilings is joint with Natalie Frank and Sam Webster, and my work on spectral triples is joint with Michael Mampusti.

08/12/2016 1:00 PMMaths 203Stephan Mescher (QMUL)Hochschild homology of Morse cochain complexes and free loop spaces (this is a joint Geometry and Analysis  Stochastic
A theorem by J.D.S. Jones from 1987 identifies the cohomology of the free loop space of a simply connected space with the Hochschild homology of the singular cochain algebra of this space. There are very strong relations between the Floer homology of cotangent bundles in symplectic geometry and the homology of free loop spaces of closed manifolds. In the light of these connections, one wants to have a geometric and Morsetheoretic identification of free loop space cohomology and the Hochschild homology of Morse cochain algebras in order to establish relations between Floer homology and Hochschild homology. After describing the underlying Morsetheoretic constructions and especially the Hochschild homology of Morse cochains, I will sketch a purely Morsetheoretic version of Jones' map and discuss its most important properties.
If time permits, I will further discuss compatibility results with product structures like the ChasSullivan loop product and give explicit Morsetheoretic descriptions of products in Hochschild cohomology in terms of gradient flow trees. 
06/12/2016 3:00 PMMaths 203Volker Schlue (Paris)On the stability of Schwarzschild de Sitter cosmologies
In general relativity, the Kerr de Sitter spacetimes are models of black holes in an expanding universe. In this talk I will discuss my current understanding of the dynamics of nearby solutions to the Einstein equations with positive cosmological constant, and show in particular that in the cosmological region the conformal Weyl curvature decays in a sufficiently general setting. I will relate my work to recent results of Hintz and Vasy, and early work on the stability of de Sitter by Friedrich.

29/11/2016 3:00 PMMaths 203Anna Fino (Turin)The symplectic CalabiYau problem for torus bundles and generalized MongeAmpere equations

22/11/2016 3:00 PMMaths 203Or Hershkovits (Stanford)Mean curvature flow of Reifenberg sets

15/11/2016 3:00 PMMaths 203Miles Simon (Magdeburg)A new local result for the Ricci flow
We present a new (2016) local result for the Ricci flow and explain the proof thereof. Joint work with Peter Topping.

18/10/2016 3:00 PMMaths 203Selcuk Barlak (Odense)Classification of simple, nuclear C*algebras and the universal coefficient theorem
A C*algebra is a closed *subalgebra of the algebra of bounded linear operators on some Hilbert space.
Originally considered for the purpose of a mathematical description of quantum mechanics, C*algebras
in their own right have been studied extensively, especially since their abstract characterization by
Gelfand and Naimark in 1943. Nuclear C*algebras form a prominent subclass, characterized either in terms of
a certain finite dimensional approximation property, or equivalently, as those C*algebras that are
amenable as Banach algebras. Very recently, by work of many hands over several years, a big class of
separable, simple, nuclear C*algebras satisfying further technical regularity properties has been classified
successfully in terms of Ktheoretical data. In this talk, I will outline these results and point out the probably
most mysterious of these regularity properties: the universal coefficient theorem (UCT) by Rosenberg
and Schochet. I will then present recent joint work with Xin Li on the question which nuclear C*algebras satisfy
the UCT. 
04/10/2016 3:00 PMMaths 203Reto Buzano (QMUL)The moduli space of 2convex embedded spheres
We investigate the topology of the space of smoothly embedded nspheres in R^{n+1}. By Smale’s theorem, this space is contractible for n=1 and by Hatcher’s proof of the Smale conjecture, it is also contractible for n=2. These results are of great importance, generalising in particular the Schoenflies theorem and Cerf’s theorem. In this talk, I will explain how geometric analysis can be used to study a higherdimensional variant of these results. The main theorem (joint with Robert Haslhofer and Or Hershkovits) states that the space of 2convex embedded spheres is pathconnected in every dimension n. The proof uses mean curvature flow with surgery.

27/09/2016 3:00 PMMaths 203Martin Taylor (Imperial)Global nonlinear stability of Minkowski space for the massless EinsteinVlasov system
Massless collisionless matter is described in general relativity by the massless EinsteinVlasov system. I will present key steps in a proof that, for asymptotically flat Cauchy data for this system, sufficiently close to that of the trivial solution, Minkowski space, the resulting maximal development of the data exists globally in time and asymptotically decays appropriately. By appealing to the corresponding result for the vacuum Einstein equations, a monumental result first obtained by ChristodoulouKlainerman in the early '90s, the proof reduces to a semiglobal problem. A key step is to gain a priori control over certain Jacobi fields on the mass shell, a submanifold of the tangent bundle of the spacetime endowed with the Sasaki metric.

02/08/2016 4:00 PMM203Sergey Matveev (Chelyabinsk State University)Prime decompositions of topological objects
In 1942 M. H. A. Newman formulated and proved a simple lemma of great importance for various fields of mathematics, including algebra and the theory of Groebner–Shirshov bases. Later it was called the Diamond Lemma, since its key construction was illustrated by a diamondshaped diagram. In the talk we will describe a new version of this lemma suitable for topological applications. Using it, we prove several results on the existence and uniqueness of prime decompositions of various topological objects: threedimensional manifolds, knots in thickened surfaces, knotted graphs, threedimensional orbifolds, knotted thetacurves in 3manifolds. As it turned out, all these topological objects admit a prime decomposition, although in some cases it is not unique.

10/06/2016 2:00 PMM103Jean Renault (Orleans)Random walks on Bratteli diagrams
Bratteli diagrams are closely related to AF algebras and provide a convenient description of privileged states such as traces and Gibbs states. In view of applications to random walks on locally compact groups and groupoids, I shall define topological Bratteli diagrams. Markov measures will be identified as a class of quasiinvariant measures. The Poisson boundary of a random walk can be studied in this context. This is a work in progress with T. Giordano.

31/05/2017 3:00 PMM103Veronique Fischer University of BathPseudodifferential operators on Lie groups
In this talk, I will present some recent developments in the theory of pseudodifferential operators on Lie groups. I will discuss first the case of R^n and the torus and then give a brief overview of the analysis in the context of Lie groups. I will conclude with some recent works developing pseudodifferential calculi on certain classes of Lie groups.

08/03/2016 3:00 PMM103Shabnam Beheshti (QMUL)MSCOs: Astrophysics Meets Algebraic Geometry?
Marginally stable circular orbits, or MSCOs, play an important role in our understanding of astrophysical phenomena (e.g., matter configurations in accretion, motion around neutron stars). We derive a necessary condition for the existence of MSCOs for stationary axisymmetric spacetimes using, unexpectedly, a tool from algebraic geometry: resultants. This yields a concrete algorithm for determining MSCOs, which we demonstrate using several examples of physical interest. No prior knowledge of astrophysics or algebraic geometry is assumed and we shall provide definitions and discussion along the way.

01/03/2016 3:00 PMM103Carlos Siqueira (Imperial College London)Hausdorff dimension of solenoidal Julia sets
Using the technique of holomorphic motions, we study the regularity of the limit set of the oneparameter family of holomorphic correspondences (wc)^q=z^p, outlining some of the main contributions in the field in the last decades. This family is the simplest generalisation of the quadratic family z^2+c. In the quasi postcritically finite case, the limit set splits into a repeller and an attractor: the usual Julia set (closure of repelling periodic points) and the dual Julia set (closure of attracting periodic points). Conformal iterated function systems hidden in the dynamics of this correspondence appear naturally in the form of dual Julia sets. We also estimate the Hausdorff dimension of the Julia set using the formalism of Gibbs states.

23/02/2016 3:00 PMM103Guenter Radons (TU Chemnitz)Nonlinear dynamics of systems with timevarying delay and its relevance for modern machining processes (joint Analysis a
Delay differential equations provide wellknown models for many processes in
nature and technology. While models with constant delay are a reasonable and
much investigated starting point for many applications, it is also clear
that in reality delays fluctuate naturally and often can be influenced to
vary systematically. Despite its high, practical relevance, the consequences
of such timevarying delays is still poorly understood. I first introduce
into the general topic of delay systems and subsequently elaborate the
relevant developments in machining applications, such as turning and
milling. Finally I report on our own recent results, which reach from
applications in machining to fundamental aspects of systems with
timevarying delay. 
16/02/2016 3:00 PMM103Cyril Houdayer (Université ParisSud)Biexact groups, strongly ergodic actions and group measure space factors with no central sequence
I will report on some recent joint work with Yusuke Isono in which we investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras arising from arbitrary actions of biexact discrete groups (e.g. free groups) on amenable von Neumann algebras. I will first explain a general spectral gap rigidity result inside such crossed product von Neumann algebras. I will then show that group measure space factors arising from strongly ergodic essentially free nonsingular actions of biexact discrete groups on standard probability spaces are full, that is, they have no nontrivial central sequence. I will finally explain how to use recent results of BoutonnetIoanaSalehi Golsefidy (2015) to construct examples of group measure space type III factors which are full and of any possible type III$_\lambda$ with $0 < \lambda \leq 1$.

16/02/2016 2:00 PMM410Yuhei Suzuki (University of Tokyo)Minimal ambient nuclear C*algebras
A deep theorem of Kirchberg showed that any separable exact C*algebra admits an ambient nuclear C*algebra.
In this talk, we investigate how can an ambient nuclear C*algebra of a given C*algebra be "tight".
For certain group C*algebras, we construct surprisingly tight ambient nuclear C*algebras.
This in particular gives the first examples of minimal ambient nuclear C*algebras of nonnuclear C*algebras.
For this purpose, we study generic behaviors of Cantor systems. 
09/02/2016 3:00 PMM103Ivan Tomasic (QMUL)Difference algebras occurring in symbolic dynamics and some questions for C*algebraists
We will discuss the correspondence between certain difference algebras and subshifts of finite type as studied in symbolic dynamics. We will relate the difference algebra of a subshift of finite type to its C*algebra and pose a few questions in this context.

02/02/2016 1:34 PMM103Reto Buzano (QMUL)Curvature quantisation for minimal hypersurfaces with bounded index and area
Given a sequence of closed minimal hypersurfaces of bounded area and index, we
prove that the total curvature along the sequence is quantised in terms of the total curvature
of some limit hypersurface, plus a sum of total curvatures of complete properly embedded
minimal hypersurfaces in Euclidean space. This yields qualitative control on the geometry
and the topology of the hypersurfaces and thus for the class of all minimal hypersurfaces with
bounded index and area. This is joint work with Ben Sharp. 
26/01/2016 3:00 PMM103Dmitri Panov (King's College London)Spherical metrics with conical singularities on S^2
I will describe a joint work with Gabirele Mondello, where we study the following question: what are possible conical angles of a curvature one metric with conical singularities on S^2?

19/01/2016 3:00 PMM103Stephanie Nivoche (Nice)A problem of Kolmogorov on the epsilonentropy
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15/12/2015 3:00 PMM103Gandalf Lechner (Cardiff)Singular values of Hardy space operators and relative commutants of von Neumann algebras
In twodimensional Minkowski space, integrable quantum field
theories can be constructed from a scattering function and a
corresponding inclusion of von Neumann algebras, related to quantum
fields localized in Rindler wedges. In this setting, the solution of the
inverse scattering problem (i.e. the construction of the field theory
from its scattering data) is intimately connected with the analysis of
the relative commutant of this inclusion.This talk will focus on an explanation how this can be done with the
help of complex analysis  more precisely, by studying the decay rate of
the singular values of certain composition and restriction operators on
Hardy spaces over tube domains. 
08/12/2015 3:00 PMM103Titus Hilberdink (Reading)Abscissae of functions related to a class of problems of analytic number theory

01/12/2015 3:00 PMM103Anton Isopoussu (Cambridge)Kstability and families of polarised varieties
The theory of Kstability provides a means of studying the canonical metric problem on polarised varieties using methods of algebraic geometry. We give a short introduction of the theory and examples of its use. Test configurations are a central concept: A projective manifold is said to be Kstable if there does not exist a destabilising test configuration. We also introduce the notions of Kstability relative to a base variety, which recovers several known examples using elementary constructions. Finally, we define a convex combination operation on the set of test configurations.

24/11/2015 3:00 PMM103Huy Nguyen (Queensland, Australia)Conformal Immersions into Riemannian Manifolds

17/11/2015 3:00 PMM103Gaiane Panina (Saint Petersburg)Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle
Robin Forman’s discrete Morse theory is a powerful technique (at least as powerful as the smooth Morse is): it allows to compute homologies, cupproduct, Novikov homologies, develop Witten’s deformation of the Laplacian, etc. In the talk we demonstrate how it works: we build a perfect discrete Morse function on the configuration space of a flexible polygon. The starting point of our construction is a cellulation of the moduli space of a planar polygonal nlinkage.

03/11/2015 3:00 PMM103Cécile Huneau (Cambridge)Stability in exponential time of Minkowski spacetime with a spacelike translation symmetry
In the presence of such a spacelike translation Killing field, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein equations with a scalar field. In generalized wave coordinates, Einstein equations can be written as a system of quasilinear quadratic wave equations. The main difficulty to prove global existence of solutions is due to the decay of free solutions to the wave equation in 2+1 dimensions which is weaker than in 3+1 dimensions. As in the work of Lindblad and Rodnianski, we have to rely on the particular structure of Einstein equations in wave coordinates. We also have to carefully chose an approximate solution with a non trivial behaviour at spacelike infinity, and a wellsuited wave gauge, to enforce convergence to Minkowski spacetime at timelike infinity.

27/10/2015 3:00 PMM103Panagiotis Gianniotis (UCL)The size of the singular set of a Type I Ricci flow

20/10/2015 4:00 PMM103A. Helemskii Moscow State UniversityHomologically best modules in classical and quantum functional analysis

13/10/2015 4:00 PMM103Gustav Holzegel (Imperial)Recent Progress in the Black Hole Stability Problem
I will review some recent progress in the black hole stability problem including a proof of the linear stability of the Schwarzschild spacetime under gravitational perturbations (joint work with Dafermos and Rodnianski).

29/09/2015 4:00 PMM103Takuya Takeishi (University of Tokyo)Primitive Ideals of BostConnes C*algebras
There are several attempts to construct C*algebras from number field, and those constructions give an interesting family of nonsimple C*algebras.
BostConnes C*algebra is the origin of those attempts, which is constructed using class field theory.
It turned out that the structure of primitive ideals of BostConnes C*algebras is related to primes of original number field.
In this talk, I would like to explain the relation and an application to classify those C*algebras. 
22/09/2015 5:30 PMM103Stuart White (University of Glasgow)C*rigidity and Bieberbach groups
The construction of operator algebras from groups goes back to the foundational work of Murray and von Neumann. Rigidity asks how much of the group is remembered by the operator algebra. The last 5 years have seen dramatic progress in the setting of von Neumann algebras with the first von Neumann rigid groups being constructed by Ioana, Popa and Vaes. I'll review these results, and then discuss the setting of C*algebras, giving examples of nonabelian torsion free C*rigid groups. This is joint work with Søren Kundby and Hannes Thiel.

22/09/2015 3:30 PMM103Xin Li (QMUL)Cartan subalgebras in C*algebras and continuous orbit equivalence for topological dynamics
This talk is about Cartan subalgebras in C*algebras, and continuous orbit equivalence for topological dynamical systems. These two notions build bridges between operator algebras, topological dynamics, and geometric group theory. Moreover, we explore rigidity phenomena for continuous orbit equivalence. Along the way, we discuss continuous cocycle rigidity for topological dynamics.

22/09/2015 12:30 PMM103Wilhelm Winter (University of Muenster)QDQ vs. UCT
I will explain a recent joint result with Aaron Tikuisis and Stuart White, saying that faithful traces on separable nuclear C*algebras which satisfy the universal coefficient theorem are quasidiagonal. This confirms Rosenberg’s conjecture that discrete amenable groups have quasidiagonal C*algebras. It also resolves the BlackadarKirchberg problem in the simple UCT case. Moreover, there are several consequences for Elliott’s classification programme; in particular, the classification of separable, simple, unital, nuclear, Zstable C*algebras with at most one trace and satisfying the UCT is now complete; the invariant in this case is ordered Ktheory.

31/03/2015 4:00 PMM103David O’Sullivan, University of SheffieldC*categories as bridges between algebra, geometry and analysis
In many cases the construction of a C*algebra from an associated algebraic or geometric object involves making an arbitrary choice of Hilbert space (satisfying certain criteria) and considering operators on that Hilbert space possessing properties determined by the algebraic or geometric structure.
A C*category is a generalisation of a C*algebra in the same way that a groupoid is a generalisation of a group. An extension of the GNSconstruction and the associated GelfandNaimark Theorem tells us that they are precisely the normclosed, *closed subcategories of the category of all Hilbert spaces and bounded linear maps between them. In cases such as outlined above, it is more natural to construct a C*category rather than a C*algebra, which amounts to considering all suitable Hilbert spaces at once.
This talk is meant as an introduction to C*categories and an overview of the basic theory. I will demonstrate how C*categories form the bridges described in the title, using as examples groupoids  both discrete (algebra) and topological (geometry). I will also say a little about how we can use Banach bundles to provide a formal characterisation of "continuous C*category" and describe how this relates to Fell bundles over topological groupoids. Time permitting, I will also say something about the construction of Ktheory for C*categories.

24/03/2015 3:00 PMM103Shaun Bullett, QMULMandelbrot Sets for Matings
I will report on joint work with Luna Lomonaco (Sao Paolo). The classical Mandelbrot set M is the subset of parameter space for which the Julia set of the quadratic polynomial z^2 + c is connected. Two analogous connectivity loci are M_1 for the family of rational maps of the form z+1/z+A (containing the matings of z^2+c with z^2+1/4) and M_corr for the family of quadratic holomorphic correspondences which are matings between polynomials z^2+c and the modular group PSL(2,Z).
Theorem 1 (SB+LL, 2015): M_corr is homeomorphic to M_1.
In our 1994 article introducing the matings between z^2+c and the modular group, Chris Penrose and I conjectured that M_corr is homeomorphic to the classical Mandelbrot set M. By Theorem 1 this becomes equivalent to the wellsupported conjecture that M_1 is homeomorphic to M.
In the talk I will outline the main steps in the proof of Theorem 1, focussing in particular on a new Yoccoz inequality for the family of correspondences.

18/03/2015 3:00 PMM103Joachim Cuntz, University of MuensterIndex theorems in the framework of bivariant KTheory
We sketch a very short proof for the index theorem by BaumDouglasTaylor and explain how this implies the index theorems by Kasparov and AtiyahSinger.

17/03/2015 3:00 PMM103Arkady Vaintrob OregonA factorization of the Alexander invariant of links using the Kontsevich integral

10/03/2015 3:00 PMM103Raymond Vozzo, University of AdelaideString structures on homogeneous spaces
In many areas of geometry and physics we often require that the manifolds we work with carry a spin structure, that is a lift of the structure group of the tangent bundle from SO(n) to its simply connected cover Spin(n). In string theory and in higher geometry the analogue is to ask for a string structure; this is a further lift of the structure group to the 3connected group String(n). Waldorf has given a way to describe string structures in terms of bundle gerbes (which are the abelian objects in higher geometry—a sort of categorification of a line bundle). Unfortunately, explicit examples are lacking. In this talk I will explain how all this works and give some examples of such structures. I will also explain some current work in progress on the geometry of string structures. This is joint work with David Roberts.

03/03/2015 3:00 PMM103Jörg Neunhäuserer Leuphana University LüneburgDimension theory of representations of real numbers

24/02/2015 3:00 PMM103Melanie Rupflin LeipzigTeichmüller harmonic map flow from cylinders
Teichmüller harmonic map flow is a gradient flow of the Dirichlet energy which is designed to evolve parametrised surfaces towards critical points of the Area.
In this talk we will discuss how to flow cylindrical surfaces in Euclidian with given boundary curves to a solution of the DouglasPlateauProblem of finding a minimal surface that spans the two given boundary curves. 
17/02/2015 3:00 PMM103Michael Farber, QMULGeometry of large random spaces and groups

03/02/2015 3:00 PMM103Reto Mueller QMULThe ChernGaussBonnet formula for singular noncompact fourdimensional manifolds
A generalisation of the classical GaussBonnet theorem to higherdimensional compact Riemannian manifolds was discovered by Chern and has been known for over fifty years. However, very little is known about the corresponding formula for complete or singular Riemannian manifolds. In this talk, we explain a new ChernGaussBonnet theorem for a class of 4dimensional manifolds with finitely many conformally flat ends and singular points. More precisely, under the assumptions of finite total Q curvature and positive scalar curvature at the ends and at the singularities, we obtain a ChernGaussBonnet type formula with error terms that can be expressed as isoperimetric deficits. This is joint work with Huy The Nguyen.

27/01/2015 3:00 PMM103Shabnam Beheshti, QMULHarmonic Maps and the Xanthopoulos Conjecture
Integrable harmonic maps have provided deep insight into important mathematical and physical problems, appearing in settings ranging from classical complex analysis to supergravity. In this talk, we shall answer the question "when is a harmonic map integrable?" by providing a theorem for a class of harmonic maps having noncompact symmetric space targets. An immediate corollary recovers classical results of Zakharov and Belinski/Alekseev for the stationary, axisymmetric Einstein vacuum/EinsteinMaxwell equations.
In conjunction with previous work on compact targets by Uhlenbeck and Terng, the techniques may illuminate our understanding of other geometric field theories as well as suggest the first inroads in answering the Xanthopoulos conjecture.
This is joint work with S. TahvildarZadeh.

20/01/2015 3:00 PMM103Bill Harvey King's College LondonHyperbolic 3manifolds and their automorphism groups
We know from the recent results of Kahn and Markovic that every compact hyperbolic 3manifold
has a finite cover with a very special structure, fibering over the circle with fibre a compact surface of genus at least 2. I will discuss these manifolds and explain why that their automorphism groups are a very restricted class of finite group. This contrasts strongly with the situation for hyperbolic surfaces. 
13/01/2015 12:15 PMM103Ben Sharp ImperialCompactness theorems for minimal hypersurfaces with bounded index
I will present a new compactness theorem for minimal hypersurfaces embedded in a closed Riemannian manifold N^{n+1} with n<7. When n=2 and N has positive Ricci curvature, Choi and Schoen proved that a sequence of minimal hypersurfaces with bounded genus converges smoothly and graphically to some minimal limit. A corollary of our main theorem recovers the result of ChoiSchoen and extends this appropriately for n<7.

09/12/2014 3:00 PMM103Joachim Zacharias, GlasgowNoncommutative covering dimension for C*algebras and dynamical systems
Various noncommutative generalisations of dimension have been considered and studied in the past decades. In recent years certain new dimension concepts for noncommutative C*algebras, called nuclear dimension and a related dimension concept for dynamical systems, called Rokhlin dimension have been defined and studied. They play an important role in the classification programme. The theory is geared towards the class of nuclear C*algebras and generalises the concept of covering dimension, in case of dynamical systems a type of equivariant covering dimension of topological spaces with a group action. There are interesting connections between coarse geometry and Rokhlin dimension. We will give an introduction to these concepts and survey some applications and connections between them.
(in collaboration with Hirshberg, Szabo, Winter, Wu)

02/12/2014 3:00 PMM103Huy Nguyen University of Queensland, AustraliaEnergy identity for sequences of minimising conformal immersions

25/11/2014 3:00 PMM103Shabnam Beheshti, QMULVignettes of Integrability
In the past four decades, the theory of integrable partial differential equations has had a rich and varied impact on both mathematics and physics. We shall survey the broad reach of integrability techniques into other mathematical disciplines through concrete examples, ranging from construction of singular solutions to Einstein’s Equations (using harmonic maps into symmetric spaces) to description of shallowwater wave interactions by way of combinatorial structures (such as Grassmann necklaces and Young diagrams). Recent joint work and open questions will be toured along the way.
This talk is intended for nonspecialists and graduate students are also welcome.

21/10/2014 4:00 PMM103Laurent Stolovitch NiceIntroduction to normal form and rigidity problems of analytic vector fields near a fixed pointSeminar series:
After a short introduction to normal form problems of analytic vector fields we will give an answer to the following problem. Let S be a homogeneous polynomial vector field and let X be an analytic perturbation of S by higher order terms. If X is formally conjugated to S, is it also analytically conjugated to it? When S is linear (and "diagonal"), the answer is due to Siegel and involves the analysis of the so called "small divisors".

14/10/2014 4:00 PMM103Lu Wang ImperialA Sharp Lower Bound for the Entropy of Closed Hypersurfaces up to Dimension SixSeminar series:
Mean curvature flow (MCF) is a deformation of the area of hypersurfaces in the steepest way. The entropy of a hypersurface is the supremum of the Gaussian surface area of all translates and scalings of the hypersurface. It is monotone decreasing under MCF and so indicates important information about the dynamics of the flow. In this talk, we will use weak MCF to show that the round sphere uniquely minimizes the entropy of closed hypersurfaces up to dimension six. This is joint work with Jacob Bernstein.

07/10/2014 4:00 PMM103Oscar Bandtlow, QMULTransfer operators for dynamical systems with holesSeminar series:
Transfer operators play an important role in the study of chaotic dynamical systems. Spectral properties of these operators yield insight into dynamical and geometric invariants of the underlying system. In this talk I will focus on transfer operators associated with dynamical systems with holes and will discuss a recent result with H.H. Rugh on the regularity of the leading eigenvalue as a function of hole size and position.

30/09/2014 4:00 PMM103Juan Valiente Kroon QMULConformal methods in General RelativitySeminar series:
In this talk I will give a brief overview of methods for the analysis of global solutions to the equations of General Relativity  the Einstein field equations. In particular, I will discuss how the notion of conformal transformations can be used to rephrase questions about global existence into questions of local existence of solutions to the Einstein field equations. I will exemplify this method with the proof of the nonlinear stability of the de Sitter spacetime. This talk is aimed at nonspecialists.

25/03/2014 3:00 PMM103Andre Neves Imperial, LondonWillmore conjecture, links and minimal surfaces

18/03/2014 3:00 PMM103Joan Bosa GlasgowThe category Cu: which maps are the correct ones? *homomorphisms or cpc order zero maps?Seminar series:
In this talk we focus on the fact that the map induced by a cpc order zero map in the category Cu does not preserve the compactly containment relation. In particular, these kinds of maps are not in the category Cu, so that in general, they may not be used in the classification of C*algebras via the Cuntz Semigroup. Nevertheless, there is a subclass of these maps which preserves the relation, and so they can be used in the above mentioned classification. Our main result characterizes these maps via the positive element induced by the description of cpc order zero maps shown by Winter and Zacharias.

11/03/2014 3:00 PMM103Christian Voigt GlasgowQuantum automorphism groups and Ktheory
Seminar series:
Geometry and AnalysisIn this talk I will first motivate and explain the definition of quantum automorphisms of finite dimensional
C*algebras, leading to compact quantum groups in the sense of Woronowicz. In the second part of the talk I will explain a general strategy how to compute their Ktheory using methods from the BaumConnes
conjecture. 
11/02/2014 3:00 PMM103Les Bunce University of ReadingJordan operator spacesSeminar series:

04/02/2014 3:00 AMM103Zinaida Lykova NewcastleUponTyneExtremal holomorphic maps on the symmetrised bidiscSeminar series:
We introduce the class of nextremal holomorphic maps, a class that generalises both finite Blaschke products and complex geodesics, and apply the notion to the finite interpolation problem for analytic functions from the
open unit disc into the symmetrised bidisc . We show that a wellknown necessary condition for the solvability of such an interpolation problem is not sufficient whenever the number of interpolation nodes is 3 or greater.
We introduce a sequence $C_n (n \geq 0)$ ; of necessary conditions for solvability, prove that they are of strictly increasing strength and show that $C_{n3}$ is insufficient for the solvability of an npoint problem for $ n \geq 3$.We introduce a classification of rational $\Gamma$inner functions, that is, analytic functions from the disc into $\Gamma$ whose radial limits at almost all points on the unit circle lie in the distinguished boundary of $\Gamma$. The classes are related to nextremality and the conditions $C_\nu$; we present numerous strict inclusions
between the classes. The talk is based on a joint work with Jim Agler and N. J. Young. 
28/01/2014 3:00 PMM103ChoHo Chu Queen Mary, LondonHarmonic functions on hypergroupsSeminar series:

14/01/2014 3:00 PMM103Huy Nguyen Queensland, AustraliaGeometric rigidity of conformal immersions of surfacesSeminar series:
We consider surfaces conformally immersed in R^3 with L^2 bounds on the norm of the second
fundamental form. In particular we will study the Liouville equation for such surfaces and give an extension
of the Classical GaussBonnet formula for surfaces and study its behaviour under conformal transformations
of Euclidean space.
We will then classify certain limit cases of these bounds, for example we will suitably generalise Osserman’s
classification of complete noncompact minimal surfaces with total curvature equal to 8\pi to the case of
complete noncompact surfaces with total bounded curvature. 
03/12/2013 3:00 PMM103Xin Li Queen MaryAmenability for groups, semigroups and C*algebrasSeminar series:

19/11/2013 3:00 PMM103Shahn Majid Queen MarySemiquantisation functor and Poisson geometry

12/11/2013 3:00 PMM103Lei Li Nankai University, ChinaOrder isomorphisms between function spacesSeminar series:

05/11/2013 3:00 AMM103Mike Rigby Queen MaryIteration of selfmaps on products of Hilbert balls

29/10/2013 3:00 PMM103John Maitland Wright Aberdeen/OxfordMonotone complete C*algebras and generic dynamicsSeminar series:

22/10/2013 4:00 PMM103Julia Slipantschuk Queen MarySpectral structure of transfer operators for expanding circle maps

15/10/2013 4:00 AMM103Reto Mueller Queen MaryThe Formation of Singularities in the Ricci Flow (II)Seminar series:
In this talk, we will explain how Perelman's entropy functional for the Ricci Flow can be used
to give a proof of Hamilton's conjecture, stating that socalled "Type I singularity models" are
gradient shrinking solitons. Our proof, obtained in joint work with Carlo Mantegazza, combines
geometric ideas with new analytic estimates such as new Gaussian heat kernel bounds on evolving
manifolds. While this is formally a continuation of our more introductory talk in the Pure Maths
Colloquium on Monday, October 14, we attempt to make this lecture completely selfcontained. 
24/09/2014 4:00 PMM103Andrew Lutken OsloModular symmetries in conducting materials

28/05/2013 4:00 PMM203Yemon Choi University of SaskatchewanCommutative amenable subalgebras of B(H)  a partial surveySeminar series:
Amenability of a Banach algebra may be thought of as an
infinitedimensional replacement for certain splitting properties that are fundamental to the study of finitedimensional algebras. If H is a Hilbert space, then by deep work of several authors, we know exactly which selfadjoint subalgebras of B(H) are amenable. In particular, all commutative selfadjoint subalgebras are amenable.This last statement is false if we drop the words "selfadjoint", and it has been an open problem for many years now to characterize the commutative amenable subalgebras of B(H). In this talk, I will present some of the background to this problem, and try to give an overview of the known results to date, obtained in papers of Sheinberg, Curtis, Loy, Willis, Gifford, Marcoux, and myself.

07/05/2013 4:00 PMM203Consuelo Martinez University of OviedoRepresentation theory of Jordan superalgebras (LMS lecture)Seminar series:
When looking at classification results of Jordan algebras and superalgebras, one would notice that "new examples" appear in simple Jordan superalgebras that do not have a counterpart in algebras. Of special interest is the case of prime characteristic and nonsemisimple even part. There are also several important differences between the representation theory of Jordan algebras and that of Jordan superalgebras.
The aim of this talk is to offer a general view of Jordan superalgebras, the
classificantion results and representation theory, emphasizing similarities and differences in the behaviour of algebras and superalgebras. 
12/03/2013 3:00 PMM203Oscar Bandtlow, Queen Mary, LondonQuantitative spectral perturbation theory for compact operatorsSeminar series:

26/02/2013 3:00 PMM203ChoHo Chu Queen Mary, LondonSymmetric Siegel domainsSeminar series:

12/02/2013 3:00 PMM203Marten Wortel University of KentDynamics of selfmaps on conesSeminar series:

05/02/2013 3:00 PMM203Dandan Yang University of YorkFree idempotentgenerated semigroups

22/01/2013 3:00 PMM203Shaun Bullett Queen Mary, LondonDiscreteness in holomorphic dynamicsSeminar series:
In a talk in the first semester entitled "Matings and discreteness
in holomorphic dynamics" I discussed various examples of "matings"
but did not have time to address the second topic. Today I will
talk about what we might mean by "discreteness" in the context of
actions of holomorphic systems on the Riemann sphere, and investigate
the "discreteness locus" for certain parameterised families of
Kleinian groups and holomorphic correspondences. 
15/01/2013 3:00 PMM203Boumediene Hamzi Imperial CollegeOn Control and Random Dynamical Systems in Reproducing Kernel Hilbert SpacesSeminar series:
We introduce a databased approach to estimating key quantities
which arise in the study of nonlinear control systems and random nonlinear
dynamical systems. Our approach hinges on the observation that much of the
existing linear theory may be readily extended to nonlinear systems  with
a reasonable expectation of success  once the nonlinear system has been
mapped into a high or infinite dimensional Reproducing Kernel Hilbert
Space. In particular, we develop computable, nonparametric estimators
approximating controllability and observability energy functions for
nonlinear systems, and study the ellipsoids they induce. It is then shown
that the controllability energy estimator provides a key means for
approximating the invariant measure of an ergodic, stochastically forced
nonlinear system. We also apply this approach to the problem of model
reduction of nonlinear control systems. In all cases the relevant
quantities are estimated from simulated or observed data. These results
collectively argue that there is a reasonable passage from linear dynamical
systems theory to a databased nonlinear dynamical systems theory through
reproducing kernel Hilbert spaces. This is joint work with J. Bouvrie (MIT). 
04/12/2012 3:00 PMM203Mike Rigby(Queen Mary, London)Cartan domainsSeminar series:

27/11/2011 3:00 PMM203Antonio Peralta(University of Granada)On the facial structure of the unit ball of a JB*triple and its dual spaceSeminar series:
We shall present some recent solutions to problems which have
been open for over twenty ve years. We refer to the problems of
describing the normclosed faces of the (closed) unit ball of a JBtriple
E and the weakclosed faces of the closed unit ball of E. Around
twenty three years ago, C. Akemann and G.K. Pedersen described the
structure of normclosed faces of the unit ball of a Calgebra A, and
the weakclosed faces of the unit ball of A, in terms of the \compact"
partial isometries in A. Three years earlier, C.M. Edwards and G.T.
Ruttimann gave a complete description of the weakclosed faces of
the unit ball of a JBWtriple, and in particular, in a von Neumann
algebra. However, the question whether the normclosed (respectively,
weakclosed) faces of the unit ball in a JBtriple E (respectively, E)
are determined by the \compact" tripotents in E has remained open.
We shall survey the positive answers established by C.M. Edwards, F.J.
FernndezPolo, C. Hoskin and the author of this talk in recent papers. 
20/11/2012 3:00 PMM203Martin Edwards(University of Oxford)Some recent developments in the structure theory of JBW*triplesSeminar series:

13/11/2012 3:00 PMM203Bas Lemmens(University of Kent)From hyperbolic geometry to nonlinear PerronFrobenius theorySeminar series:
This talk concerns the applications of Hilbert's metric in operator theory and in dynamics of nonlinear operators.

30/10/2012 3:00 PMM203ChoHo Chu (Queen Mary, London)Geometry of a Lie ballSeminar series:

16/10/2012 4:00 PMM203Shaun Bullett (Queen Mary, London)Matings and discreteness in holomorphic dynamicsSeminar series:

09/10/2012 4:00 PMM203Sergey Favorov (Kharkov National University)Spectral perturbation theory, generalized convexity, and Blaschketype conditions in unbounded domainsSeminar series:

22/05/2012 4:00 PMM203Oliver Jenkinson (London)Topics in convexity theory and its applications to ergodic optimizationSeminar series:

27/03/2012 4:00 PMM203Bernard Russo (University of California)Holomorphic characterization of operator algebrasSeminar series:
Unital operator algebras are characterized up to complete isometry using only the holomorphic structures of the associated Banach spaces. This is a joint work with Matthew Neal.

20/03/2012 3:00 PMM203Stephanie Nivoche (Nice)On a problem of Kolmogorov on the epsilonentropySeminar series:
I will discuss a problem of Kolmogorov concerned with
the epsilonentropy of classes of analytic functions.
In one complex variable, this problem was solved
in the 1960s using classical potential theory. In several
complex variables it was shown in the 1980s that this problem is
equivalent to a certain problem in pluripotential theory, now called
Zahariuta's conjecture.In this talk I will discuss this conjecture and outline a strategy of proof.

13/03/2012 3:00 PMM203Oscar Bandtlow (London)Spectra of composition operators with boundary fixed pointSeminar series:

06/03/2012 3:00 PMM203Veronique Fischer(Padua/London)Global quantization of pseudodifferential operators on Lie groupsSeminar series:
Pseudodifferential operators (PDO's) are primarily defined in the familiar setting of the Euclidean space. For four decades, they have been standard tools in the study of PDE's and it is natural to attempt defining PDO's in other settings. In this talk, after discussing the concept of PDO's on the Euclidean space and on the torus, I will present some recent results and outline future work regarding PDO's on Lie groups as well as some of the applications to PDE's. This will be a joint work with Michael Ruzhansky (Imperial College London).

28/02/2012 3:00 PMM203Andrew Curtis (London)How to understand the limit sets of covering correspondences?Seminar series:

14/02/2012 3:00 PMM203Christopher Penrose (London)Equicontinuity for mixed iteration of correspondencesSeminar series:

31/01/2012 3:00 PMM203Re O'Buachalla (London)An introduction to Kahler geometrySeminar series:

24/01/2012 3:00 PMM203ChoHo Chu (London)Iterates of Mobius transformationsSeminar series:

13/12/2011 3:00 PMM203Oscar Bandtlow (London)Spectra of composition operators IISeminar series:

06/12/2011 3:00 PMM203Oscar Bandtlow (London)Spectra of composition operatorsSeminar series:

29/11/2011 3:00 PMM203Mike Rigby (London)The Wolff theorem in the planeSeminar series:

01/11/2011 3:00 PMM203Olof Sisask (London)Arithmetic progressions in sumsets via geometry, analysis and probabilitySeminar series:
We shall use a theorem of probability to prove a geometrical result, which when applied in an analytical context yields an interesting and surprisingly strong result in combinatorics on the existence of long arithmetic progressions in sums of two sets of integers.This is joint work with Ernie Croot and Izabella Laba.

25/10/2011 4:00 PMM203Veronique Fischer(Kings College London)Some invariant multipliersSeminar series:
In the Euclidean plane, it is easy to determine the smooth or Schwartz functions which are invariant under rotations, using the Fourier transform, which also gives a characterisation of the multipliers in the Laplace operator. Similar characterisations are valid for any action of a compact group on a Euclidean space by the G. Schwarz Theorem.
In this talk, I will present a study of this question in another
setting: the Heisenberg group under the action of the unitary group as
well as more general nilpotent Gelfand pairs. This is a joint work
with Fulvio Ricci and Oksana Yakimova. 
18/10/2011 4:00 PMM203ChoHo Chu (London)Iteration of holomorphic mapsSeminar series:Geometry and Analysis

27/09/2011 4:00 PMM203Anders Hansen (Cambridge)The Solvability Complexity Index and approximations of spectra of operatorsSeminar series:
In this talk we will discuss the following long standing and fundamental problem: Given an operator on a separable Hilbert space (with an orthonormal basis), can one compute/construct its spectrum from its matrix elements. As we want such a construction to be useful in application (i.e. implementable on a computer), we restrict ourselves to only allowing the use of arithmetic operations and radicals of the matrix elements and taking limits. We will give an affirmative answer to the question, and also introduce a classification tool for the complexity of different computational spectral problems, namely, the Solvability Complexity Index.

09/06/2011 5:00 PMM103KaSing Lau (Hong Kong)Martin boundary and selfsimilar setsSeminar series:

22/03/2011 3:00 PMM103MingHsiu Hsu (National Sun Yatsen University, Taiwan)Banach Lie groupsSeminar series:

15/03/2011 3:00 PMM103MingHsiu Hsu (National Sun Yatsen University, Taiwan)An introduction to Banach manifoldsSeminar series:

08/03/2011 3:00 PMM103ChoHo Chu (London)Jordan structures in geometry and analysisSeminar series:

15/02/2011 3:00 PMM103Maria Victoria Velasco (Granada, Spain)Nonassoicative Banach algebras and spectral theorySeminar series:
Nonassociative Banach algebras play an important role in many areas of modern mathematics and science, e.g. Biology, Physics,
Cellular Automata and Cryptography. Nevertheless, a nonassociative spectral theory has yet to be developed. Indeed, there is no clear idea what the spectrum of an element in a nonassociative Banach algebra should mean.The aim of this talk is to provide an overview of the situation and also to show a way to extend the classical spectral theory to the nonassociative setting. We also discuss applications of such a theory to the problem of automatic continuity of homomorphisms.

25/01/2011 3:00 PMM103Titus Hilberdink (Reading)Quasi norms for an arithmetical convolution operator and the Riemann zeta functionSeminar series:

18/01/2011 3:00 PMM103Fatemeh Bahmani (London)Ternary structures in Hilbert spacesSeminar series:

07/12/2010 3:00 PMM203Re O'Buachalla (London)The matrix exponential: an analytic introduction to Lie theorySeminar series:
The talk will be an anlytic introduction to (very) basic Lie theory. I will focus on just matrix groups, using the matrix exponential to formulate the idea of Lie algebras and then to build up a statement of the BakerCampbellHausdorff formula.

23/11/2010 3:00 PMM203Ivan Tomasic (London)The etale site of a difference schemeSeminar series:

16/11/2009 3:00 PMM203Srishti Dhar Chatterji (Lausanne)Georges de Rham, his life and timeSeminar series:
Professor Chatterji was a colleague of de Rham in Laussane and has kindly made available his article on de Rham at the website http://www.maths.qmul.ac.uk/~cchu

09/11/2010 3:00 PMM203Oscar Bandtlow (LondonA new look at an old ergodic theoremSeminar series:

02/11/2010 3:00 PMM203Mark Walters (London)Lion and Man  Can Both Win?Seminar series:
Rado introduced the following `lion and man' game in the 1930's: two
players (the lion and the man) are in the closed unit disc and they
can each run at the same speed. The lion would like to catch the man
and the man would like to avoid being captured.
This problem had a chequered history with several false proofs before
Besicovitch finally gave a correct proof.
We ask the surprising question: can both players win? 
26/10/2010 4:00 PMM203Shaun Bullett (London)Branched coverings  from Hurwitz to ThurstonSeminar series:

19/10/2010 4:00 PMM203Tirthankar Bhattacharyya (Bangalore)Abstract characteristic functionSeminar series:
Abstract: Taking cue from the group of automorphisms of the open unit disk, Sz.Nagy and Foias constructed a complete unitary invariant for a contractive operator. The relation was that a contractive operator (henceforth a contraction) on a Hilbert space has its spectrum in the closed unit disk. Using this fact, they constructed a function with its values in a certain Banach space. This function turned out to be the inavariant for a certain class of contractions (not for all contractions, for obvious reasons which will be explained in the talk).
In recent times, there has been a great deal of activity in domains more general than the disk, the unit ball in the ddimensional complex space for example, or the polydisk. This involves tuples of operators rather than a single contraction. The connection with multivariable complex analysis is fascinating. An old theorem of Schur comes in naturally.
So, in a general domain, one could consider any positive definite kernel and a tuple of operators suited to the kernel. Is there a complete unitary invariant? If so, for which class of tuples of operators? Such are the questions which will be addressed in this talk.
The talk will be self contained with no prerequisite except basic knowledge of Hilbert space operators.

12/10/2010 4:00 PMM203Shahn Majid (London)Some problems of noncommutative harmonic analysisSeminar series:

05/10/2010 3:00 PMM513ChoHo Chu (London)Cartan domains and function theorySeminar series:

23/03/2010 3:00 PMMaths 103Y. Wang (York)On Baundant semigroups

23/02/2010 3:00 PMMaths 103Eugene Shargorodsky (KCL)Level sets of the resolvent norm and pseudospectraSeminar series:

09/02/2010 3:00 PMMaths 103Oscar Bandtlow (QMUL)Resolvent growth of quasinilpotent operatorsSeminar series:

02/02/2010 3:00 PMMaths 103Alexander Pushnitski (KCL)Quantum mechanical scattering and the geometry of Hilbert spaceSeminar series:

26/01/2010 3:00 PM103Fatemeh Bahmani (QMUL)TitsKantorKoecher Lie algebrasSeminar series:

19/01/2010 3:00 PMMaths 103Maria Apazoglou (QMUL)Real and complex Jordan homomorphismsSeminar series:

15/12/2009 3:00 PMM103Jonit Fischmann (London)Complex random matrices and their eigenvalues (postponed to 2010)Seminar series:

15/12/2011 3:00 PMM103Jonit Fischmann (London)Complex random matrices and their eigenvalues (postponed to 2010)Seminar series:

10/02/2011 5:09 PMM513Richard Spinney (UCL)A Modern Treatment of Entropy Production for Simple Stochastic SystemsSeminar series:

01/12/2009 3:00 PMM103Oscar Bandtlow (London)Estimating spectral distance II

24/11/2009 3:00 PMM103Oscar Bandtlow (London)Estimating spectral distance I

10/11/2009 3:00 PMM103ChoHo Chu (London)Homogeneous balls III

03/11/2009 3:00 PMM103ChoHo Chu (London)Homogeneous balls II

27/10/2010 3:00 PMM103Hugo Touchette (London)LegendreFenchel transform of convex and nonconvex functions

20/10/2009 4:00 PMM103ChoHo Chu (London)Homogeneous balls ISeminar series:

13/10/2009 4:01 PMM103Fatemeh Bahmani (London)Isomorphisms of HilbertSchmidt operators

06/10/2009 4:00 PMM103Maria Apazoglou (London)Complexification of real isometries on C*algebras