Geometry and Analysis
Time: Tuesday at 3pm (except special events)
Location: Queens' Building, Room W316
Organisers: Arick Shao and Huy Nguyen. Please email us in case you have any questions or want to give a talk yourself.

DateRoomSpeakerTitle

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

26/10/2010 4:00 PMM203Shaun Bullett (London)Branched coverings  from Hurwitz to ThurstonSeminar 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? 
09/11/2010 3:00 PMM203Oscar Bandtlow (LondonA new look at an old ergodic theoremSeminar 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

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

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

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

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

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

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

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

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.

18/10/2011 4:00 PMM203ChoHo Chu (London)Iteration of holomorphic mapsSeminar series:Geometry and Analysis

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. 
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.

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

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

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

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

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

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

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

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

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.

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.

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

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

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

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

20/11/2012 3:00 PMM203Martin Edwards(University of Oxford)Some recent developments in the structure theory of JBW*triplesSeminar 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. 
04/12/2012 3:00 PMM203Mike Rigby(Queen Mary, London)Cartan domainsSeminar series:

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

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

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

12/03/2013 3:00 PMM203Oscar Bandtlow, Queen Mary, LondonQuantitative spectral perturbation theory for compact operatorsSeminar series:

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. 
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.

24/09/2014 4:00 PMM103Andrew Lutken OsloModular symmetries in conducting materials

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

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

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

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

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

03/12/2013 3:00 PMM103Xin Li Queen MaryAmenability for groups, semigroups and C*algebrasSeminar 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. 
28/01/2014 3:00 PMM103ChoHo Chu Queen Mary, LondonHarmonic functions on hypergroupsSeminar 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. 
11/02/2014 3:00 PMM103Les Bunce University of ReadingJordan operator spacesSeminar series:

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. 
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.

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

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.

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.

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.

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".

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.

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

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)

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.

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. 
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.

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.

17/02/2015 3:00 PMM103Michael Farber, QMULGeometry of large random spaces and groups

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

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.

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

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.

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.

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.

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.

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 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.

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. 
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).

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

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

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.

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.

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

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.

08/12/2015 3:00 PMM103Titus Hilberdink (Reading)Abscissae of functions related to a class of problems of analytic number theory

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. 
19/01/2016 3:00 PMM103Stephanie Nivoche (Nice)A problem of Kolmogorov on the epsilonentropy
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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?

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. 
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.

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. 
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 $0 < \lambda \leq 1$.

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. 
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.

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.

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.

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.

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.

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.

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.

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. 
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.

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

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

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.

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. 
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.

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

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.

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. 
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.

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.

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.

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.

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.

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).

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).

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

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 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 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

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) .

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) .

31/05/2017 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) .

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.

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. 
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.

06/12/2017 4:00 PMW316Luc Nguyen (Oxford)TBA

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 
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.

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.

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.

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).

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.

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

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.

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

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.

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.

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.

27/03/2018 3:00 PMQueens' Building, Room W316Ali Feizmohammadi (UCL)TBA
TBA

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

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.