Professor Claudia GarettoProfessor in Mathematics. Equality, Diversity and Inclusion Lead Email: c.garetto@qmul.ac.ukRoom Number: Mathematical Sciences Building, Room: MB-325ProfilePublicationsProfileI 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)ResearchPublications Shah R, Garetto C, Belafonte AD et al. (2024). Diversifying the STEM curriculum https://www.qmul.ac.uk/queenmaryacademy/educators/events-and-workshops/festival-of-education/festival-of-education-2024/ Queen Mary Festival of Education. doi https://qmro.qmul.ac.uk/xmlui/handle/123456789/99715 Garetto C, Sabitbek B (2024). Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, III: singular coefficients Mathematische Annalen nameOfConference. doi https://qmro.qmul.ac.uk/xmlui/handle/123456789/96454 Discacciati M, Garetto C, Loizou C (2023). On the Wave Equation with Space Dependent Coefficients: Singularities and Lower Order Terms Acta Applicandae Mathematicae nameOfConference. 10.1007/s10440-023-00601-6 https://qmro.qmul.ac.uk/xmlui/handle/123456789/93818 Discacciati M, Garetto C, Loizou C (2022). Inhomogeneous Wave Equation with T-Dependent Singular Coefficients Journal of Differential Equations nameOfConference. 10.1016/j.jde.2022.02.039 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/76859 Garetto C (2021). On the wave equation with multiplicities and space-dependent irregular coefficients Transactions of the American Mathematical Society nameOfConference. 10.1090/tran/8319 qmroHref 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. 10.1016/j.jde.2020.05.038 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/65044 Garetto C, Jäh C, Ruzhansky M (2018). Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posedness Mathematische Annalen nameOfConference. 10.1007/s00208-018-1672-1 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/52963 Garetto C, Ruzhansky M (2017). On C∞ well-posedness of hyperbolic systems with multiplicities Annali di Matematica Pura ed Applicata (1923 -) nameOfConference. 10.1007/s10231-017-0639-2 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/53373 Garetto C, Jäh C (2017). Well-posedness of hyperbolic systems with multiplicities and smooth coefficients Mathematische Annalen nameOfConference. 10.1007/s00208-016-1436-8 qmroHref Garetto C, Ruzhansky M (2016). On hyperbolic systems with time-dependent Hölder characteristics Annali di Matematica Pura ed Applicata nameOfConference. 10.1007/s10231-016-0567-6 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/53345 Garetto C (2015). On hyperbolic equations and systems with non-regular time dependent coefficients Journal of Differential Equations nameOfConference. 10.1016/j.jde.2015.07.011 qmroHref Garetto C, Ruzhansky M (2015). Wave equation for sums of squares on compact Lie groups Journal of Differential Equations nameOfConference. 10.1016/j.jde.2015.01.034 qmroHref Garetto C, Ruzhansky M (2015). Hyperbolic Second Order Equations with Non-Regular Time Dependent Coefficients Archive for Rational Mechanics and Analysis nameOfConference. 10.1007/s00205-014-0830-1 qmroHref Garetto C, Oberguggenberger M (2015). Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients Mathematische Nachrichten nameOfConference. 10.1002/mana.201400192 qmroHref Garetto C, Ruzhansky M (2014). A note on weakly hyperbolic equations with analytic principal part Journal of Mathematical Analysis and Applications nameOfConference. 10.1016/j.jmaa.2013.09.011 qmroHref Garetto C, Oberguggenberger M (2014). Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities Proceedings of the Edinburgh Mathematical Society nameOfConference. 10.1017/s0013091513000424 qmroHref Garetto C, Ruzhansky M (2013). Weakly hyperbolic equations with non-analytic coefficients and lower order terms Mathematische Annalen nameOfConference. 10.1007/s00208-013-0910-9 qmroHref Garetto C, Ruzhansky M (2012). On the well-posedness of weakly hyperbolic equations with time-dependent coefficients Journal of Differential Equations nameOfConference. 10.1016/j.jde.2012.05.001 qmroHref Garetto C (2011). Lp and Sobolev boundedness of pseudodifferential operators with non-regular symbol: A regularisation approach Journal of Mathematical Analysis and Applications nameOfConference. 10.1016/j.jmaa.2011.02.056 qmroHref Garetto C, Vernaeve H (2011). Hilbert C ~ \widetilde {\mathbb {C}} -modules: Structural properties and applications to variational problems Transactions of the American Mathematical Society nameOfConference. 10.1090/s0002-9947-2010-05143-8 qmroHref Garetto C (2009). Sufficient conditions of local solvability for partial differential operators on spaces of colombeau type Electronic Journal of Differential Equations nameOfConference. doi qmroHref Garetto C (2009). Closed graph and open mapping theorems for topological $ \tilde \lc $‐modules and applications Mathematische Nachrichten nameOfConference. 10.1002/mana.200610793 qmroHref Garetto C, Hörmann G, Oberguggenberger M (2009). Generalized oscillatory integrals and Fourier integral operators Proceedings of the Edinburgh Mathematical Society nameOfConference. 10.1017/s0013091506000915 qmroHref Garetto C (2008). Fundamental Solutions in the Colombeau Framework: Applications to Solvability and Regularity Theory Acta Applicandae Mathematicae nameOfConference. 10.1007/s10440-008-9220-8 qmroHref Garetto C (2008). Generalized Fourier Integral Operators on Spaces of Colombeau Type journal nameOfConference. 10.1007/978-3-7643-8969-7_8 qmroHref 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. doi qmroHref 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. 10.2298/bmat0631115g qmroHref Garetto C (2005). Topological Structures in Colombeau Algebras: Investigation of the Duals of , and Monatshefte für Mathematik nameOfConference. 10.1007/s00605-005-0331-2 qmroHref Garetto C, Gramchev T, Oberguggenberger M (2005). Pseudodifferential operators with generalized symbols and regularity theory Electronic Journal of Differential Equations nameOfConference. doi qmroHref Garetto C, Hörmann G (2005). MICROLOCAL ANALYSIS OF GENERALIZED FUNCTIONS: PSEUDODIFFERENTIAL TECHNIQUES AND PROPAGATION OF SINGULARITIES Proceedings of the Edinburgh Mathematical Society nameOfConference. 10.1017/s0013091504000148 qmroHref Garetto C (2005). Topological Structures in Colombeau Algebras: Topological -modules and Duality Theory Acta Applicandae Mathematicae nameOfConference. 10.1007/s10440-005-6700-y qmroHref Garetto C (2004). Pseudo-Differential Operators in Algebras of Generalized Functions and Global Hypoellipticity Acta Applicandae Mathematicae nameOfConference. 10.1023/b:acap.0000013814.89972.3c qmroHref