# 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), 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