Dr Claudia Garetto

Email: c.garetto@qmul.ac.uk
Room Number: Mathematical Sciences Building, Room: MB-325

Profile

I am a Mathematician working in the area of Partial Differential Equations and Mathematical Analysis. I am a Reader in the School of Mathematics at Queen Mary University of London and a Visiting Professor in the School of Mathematical Sciences at Loughborough University. Previously I have been a Junior Research Fellow at Imperial College London.

My research interests are:

• Hyperbolic equations and systems with multiplicities
• PDEs with singular coefficients and very weak solutions
• Sub-elliptic problems on compact Lie groups
• Microlocal analysis, Fourier integral operators and pseudo-differential operators
• Algebras of generalised functions

EPSRC support for my research:

EP/L026422/1: Hyperbolic systems with multiplicities (2014-2017)

EP/V005529/1: Hyperbolic problems with discontinuous coefficients (2021-2025)

Publications

• Discacciati M, Garetto C, Loizou C (2022). On the wave equation with space dependent coefficients: singularities and lower order terms journal nameOfConference.
• Discacciati M, Garetto C, Loizou C (2022). Inhomogeneous Wave Equation with T-Dependent Singular Coefficients Journal of Differential Equations nameOfConference.
• Discacciati M, Garetto C, Loizou C (2021). Inhomogeneous wave equation with $t$-dependent singular coefficients journal nameOfConference.
• Garetto C (2021). On the wave equation with multiplicities and space-dependent irregular coefficients Transactions of the American Mathematical Society nameOfConference.
• Garetto C, Jäh C, Ruzhansky M (2020). Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: microlocal analysis Journal of Differential Equations nameOfConference.
• Garetto C, Jäh C, Ruzhansky M (2020). Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: microlocal analysis journal nameOfConference.
• Garetto C, Jäh C, Ruzhansky M (2018). Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posedness Mathematische Annalen nameOfConference.
• Garetto C, Jäh C, Ruzhansky M (2018). Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I. Well-posedness journal nameOfConference.
• Garetto C, Ruzhansky M (2017). On C well-posedness of hyperbolic systems with multiplicities Annali di Matematica Pura ed Applicata nameOfConference.
• Garetto C, Jäh C (2017). Well-posedness of hyperbolic systems with multiplicities and smooth coefficients Mathematische Annalen nameOfConference.
• Garetto C, Ruzhansky M (2016). On hyperbolic systems with time-dependent Hölder characteristics Annali di Matematica Pura ed Applicata nameOfConference.
• Garetto C, Jäh C (2016). Well-posedness of hyperbolic systems with multiplicities and smooth coefficients journal nameOfConference.
• Garetto C, Ruzhansky M (2015). On $C^\infty$ well-posedness of hyperbolic systems with multiplicities journal nameOfConference.
• Garetto C (2015). On hyperbolic equations and systems with non-regular time dependent coefficients Journal of Differential Equations nameOfConference.
• Garetto C, Ruzhansky M (2015). On hyperbolic systems with time dependent Hölder characteristics journal nameOfConference.
• Garetto C, Ruzhansky M (2015). Hyperbolic Second Order Equations with Non-Regular Time Dependent Coefficients Archive for Rational Mechanics and Analysis nameOfConference.
• Garetto C, Ruzhansky M (2015). Wave equation for sums of squares on compact Lie groups Journal of Differential Equations nameOfConference.
• Garetto C, Oberguggenberger M (2015). Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients Mathematische Nachrichten nameOfConference.
• Garetto C, Ruzhansky M (2014). A note on weakly hyperbolic equations with analytic principal part Journal of Mathematical Analysis and Applications nameOfConference.
• Garetto C, Ruzhansky M (2014). Wave equation for sums of squares on compact Lie groups journal nameOfConference.
• Garetto C, Ruzhansky M (2013). Hyperbolic second order equations with non-regular time dependent coefficients journal nameOfConference.
• Garetto C, Ruzhansky M (2013). Weakly hyperbolic equations with non-analytic coefficients and lower order terms Mathematische Annalen nameOfConference.
• Garetto C, Oberguggenberger M (2013). Generalized fourier integral operator methods for hyperbolic equations with singularities Proceedings of the Edinburgh Mathematical Society nameOfConference.
• Garetto C, Ruzhansky M (2013). On weakly hyperbolic equations with analytic principal part journal nameOfConference.
• Garetto C, Ruzhansky M (2012). On the well-posedness of weakly hyperbolic equations with time-dependent coefficients Journal of Differential Equations nameOfConference.
• Garetto C, Ruzhansky M (2012). Weakly hyperbolic equations with non-analytic coefficients and lower order terms journal nameOfConference.
• Garetto C (2011). Lp and Sobolev boundedness of pseudodifferential operators with non-regular symbol: A regularisation approach Journal of Mathematical Analysis and Applications nameOfConference.
• Garetto C, Ruzhansky M (2011). On the well-posedness of weakly hyperbolic equations with time dependent coefficients journal nameOfConference.
• Garetto C, Oberguggenberger M (2011). Generalised Fourier integral operator methods for hyperbolic equations with singularities journal nameOfConference.
• Garetto C, Oberguggenberger M (2011). Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients journal nameOfConference.
• Garetto C, Vernaeve H (2011). Hilbert ℂ̃-modules: Structural properties and applications to variational problems Transactions of the American Mathematical Society nameOfConference.
• Garetto C (2009). Sufficient conditions of local solvability for partial differential operators on spaces of colombeau type Electronic Journal of Differential Equations nameOfConference.
• Garetto C (2009). Closed graph and open mapping theorems for topological ℂ̃-modules and applications Mathematische Nachrichten nameOfConference.
• Garetto C, Hörmann G, Oberguggenberger M (2009). Generalized oscillatory integrals and fourier integral operators Proceedings of the Edinburgh Mathematical Society nameOfConference.
• Garetto C (2009). Generalized Fourier integral operators on spaces of Colombeau type journal nameOfConference.
• Garetto C (2008). Fundamental solutions in the colombeau framework: Applications to solvability and regularity theory Acta Applicandae Mathematicae nameOfConference.
• Garetto C, Vernaeve H (2007). Hilbert $\widetilde{\C}$-modules: structural properties and applications to variational problems journal nameOfConference.
• Garetto C (2006). Microlocal analysis in the dual of a Colombeau algebra: Generalized wave front sets and noncharacteristic regularity New York Journal of Mathematics nameOfConference.
• Garetto C, Hoermann G, Oberguggenberger M (2006). Generalized Oscillatory Integrals and Fourier Integral Operators journal nameOfConference.
• Garetto C, Hormann G (2006). On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets Bulletin Classe des sciences mathematiques et natturalles nameOfConference.
• Garetto C (2005). Topological structures in Colombeau algebras: Investigation of the duals of script G sign c (Ω), script G sign(Ω) and script G sign script S sign (ℝ n) Monatshefte fur Mathematik nameOfConference.
• Garetto C, Gramchev T, Oberguggenberger M (2005). Pseudodifferential operators with generalized symbols and regularity theory Electronic Journal of Differential Equations nameOfConference.
• Garetto C, Hörmann G (2005). Microlocal analysis of generalized functions: Pseudodifferential techniques and propagation of singularities Proceedings of the Edinburgh Mathematical Society nameOfConference.
• Garetto C (2005). Topological structures in Colombeau algebras: Topological ℂ̃-modules and duality theory Acta Applicandae Mathematicae nameOfConference.
• Garetto C, Hoermann G (2005). On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets journal nameOfConference.
• Garetto C, Hoermann G (2004). Microlocal analysis of generalized functions: pseudodifferential techniques and propagation of singularities journal nameOfConference.
• Garetto C (2004). Pseudo-differential operators in algebras of generalized functions and global hypoellipticity Acta Applicandae Mathematicae nameOfConference.