Prof Claudia Garetto
Professor of Mathematics
Science and Engineering EDI Lead
Deputy Head of The Centre for Geometry, Analysis and Gravitation
School of Mathematical Sciences
Queen Mary University of London
Queen Mary University of London
Research
Hyperbolic equations, Low regular coefficients, Multiplicities, Generalised Solutions
Interests
Analysis of hyperbolic PDEs and systems with variable multiplicities.Co-organiser of the London Analysis and Probability Seminar.
Publications
Publications of specific relevance to the Centre for Geometry, Analysis and Gravitation2024
Shah R, Garetto C, Belafonte AD and Serrano MFP (2024). Diversifying the STEM curriculum. Queen Mary Festival of Education London, United Kingdom 6 Mar 2024 - 7 Mar 2024. 07-03-2024
Garetto C and Sabitbek B (2024). Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, III: singular coefficients. Mathematische Annalen, Springer 19-01-2024
Garetto C (2024). On Hyperbolic Equations with Space-Dependent Coefficients: C∞ Well-Posedness and Levi Conditions. Women in Analysis and PDE 163-173. 01-01-2024
2023
Discacciati M, Garetto C and Loizou C (2023). On the Wave Equation with Space Dependent Coefficients: Singularities and Lower Order Terms. Acta Applicandae Mathematicae, Springer Nature vol. 187 (1), 10-10. 13-09-2023
2022
Discacciati M, Garetto C and Loizou C (2022). Inhomogeneous Wave Equation with T-Dependent Singular Coefficients. Journal of Differential Equations 02-03-2022
2021
Garetto C (2021). On the wave equation with multiplicities and space-dependent irregular coefficients. Transactions of the American Mathematical Society, American Mathematical Society (AMS) vol. 374 (5), 3131-3176. 12-02-2021
2020
Garetto C, Jäh C and Ruzhansky M (2020). Hyperbolic systems with non-diagonalisable principal part and variable
multiplicities, II: microlocal analysis. Journal of Differential Equations, Elsevier 16-06-2020
2018
Garetto C, Jäh C and Ruzhansky M (2018). Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posedness. Mathematische Annalen, Springer Nature vol. 372 (3-4), 1597-1629. 22-03-2018
2017
Garetto C and Ruzhansky M (2017). On C∞ well-posedness of hyperbolic systems with multiplicities. Annali di Matematica Pura ed Applicata (1923 -), Springer Nature vol. 196 (5), 1819-1834. 25-02-2017
2016
Garetto C and Jäh C (2016). Well-posedness of hyperbolic systems with multiplicities and smooth coefficients. Mathematische Annalen, Springer Nature vol. 369 (1-2), 441-485. 22-06-2016
Garetto C and Ruzhansky M (2016). On hyperbolic systems with time-dependent Hölder characteristics. Annali di Matematica Pura ed Applicata vol. 196 (1), 155-164. 12-04-2016
2015
Garetto C (2015). On hyperbolic equations and systems with non-regular time dependent coefficients. Journal of Differential Equations, Elsevier vol. 259 (11), 5846-5874. 01-12-2015
Garetto C and Ruzhansky M (2015). Wave equation for sums of squares on compact Lie groups. Journal of Differential Equations, Elsevier vol. 258 (12), 4324-4347. 01-06-2015
2014
Garetto C and Ruzhansky M (2014). Hyperbolic Second Order Equations with Non-Regular Time Dependent Coefficients. Archive for Rational Mechanics and Analysis, Springer Nature vol. 217 (1), 113-154. 20-12-2014
Garetto C and Oberguggenberger M (2014). Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients. Mathematische Nachrichten, Wiley vol. 288 (2-3), 185-205. 17-11-2014
Garetto C and Ruzhansky M (2014). A note on weakly hyperbolic equations with analytic principal part. Journal of Mathematical Analysis and Applications, Elsevier vol. 412 (1), 1-14. 01-04-2014
2013
Garetto C and Oberguggenberger M (2013). Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities. Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP) vol. 57 (2), 426-463. 19-09-2013
Garetto C and Ruzhansky M (2013). Weakly hyperbolic equations with non-analytic coefficients and lower order terms. Mathematische Annalen, Springer Nature vol. 357 (2), 401-440. 05-02-2013
2012
Garetto C and Ruzhansky M (2012). On the well-posedness of weakly hyperbolic equations with time-dependent coefficients. Journal of Differential Equations, Elsevier vol. 253 (5), 1317-1340. 01-09-2012
2011
Garetto C (2011). Lp and Sobolev boundedness of pseudodifferential operators with non-regular symbol: A regularisation approach. Journal of Mathematical Analysis and Applications, Elsevier vol. 381 (1), 328-343. 01-09-2011
2010
Garetto C and Vernaeve H (2010). Hilbert C ~ \widetilde {\mathbb {C}} -modules: Structural properties and applications to variational problems. Transactions of the American Mathematical Society, American Mathematical Society (AMS) vol. 363 (4), 2047-2090. 02-11-2010
2009
Garetto C (2009). Sufficient conditions of local solvability for partial differential operators on spaces of colombeau type. Electronic Journal of Differential Equations vol. 2009, 1-43. 21-09-2009
Garetto C (2009). Closed graph and open mapping theorems for topological $ \tilde \lc $‐modules and applications. Mathematische Nachrichten, Wiley vol. 282 (8), 1159-1188. 21-07-2009
Garetto C, Hörmann G and Oberguggenberger M (2009). Generalized oscillatory integrals and Fourier integral operators. Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP) vol. 52 (2), 351-386. 28-05-2009
2008
Garetto C (2008). Fundamental Solutions in the Colombeau Framework: Applications to Solvability and Regularity Theory. Acta Applicandae Mathematicae, Springer Nature vol. 102 (2-3), 281-318. 08-02-2008
Garetto C (2008). Generalized Fourier Integral Operators on Spaces of Colombeau Type. New Developments in Pseudo-Differential Operators 137-184. 01-01-2008
2006
Garetto C (2006). Microlocal analysis in the dual of a Colombeau algebra: Generalized wave front sets and noncharacteristic regularity. New York Journal of Mathematics vol. 12, 275-318. 25-09-2006
Garetto C and 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, National Library of Serbia vol. 133 (31), 115-136. 01-01-2006
2005
Garetto C (2005). Topological Structures in Colombeau Algebras: Investigation of the Duals of , and. Monatshefte für Mathematik, Springer Nature vol. 146 (3), 203-226. 28-10-2005
Garetto C, Gramchev T and Oberguggenberger M (2005). Pseudodifferential operators with generalized symbols and regularity theory. Electronic Journal of Differential Equations vol. 2005 21-10-2005
Garetto C and Hörmann G (2005). MICROLOCAL ANALYSIS OF GENERALIZED FUNCTIONS: PSEUDODIFFERENTIAL TECHNIQUES AND PROPAGATION OF SINGULARITIES. Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP) vol. 48 (3), 603-629. 15-09-2005
Garetto C (2005). Topological Structures in Colombeau Algebras: Topological -modules and Duality Theory. Acta Applicandae Mathematicae, Springer Nature vol. 88 (1), 81-123. 01-08-2005
2004
Garetto C (2004). Pseudo-Differential Operators in Algebras of Generalized Functions and Global Hypoellipticity. Acta Applicandae Mathematicae, Springer Nature vol. 80 (2), 123-174. 01-01-2004
Grants
Grants of specific relevance to the Centre for Geometry, Analysis and GravitationHyperbolic problems with discontinuous coefficients-GRANT TRANSFERClaudia Garetto and Michael Ruzhansky
£543,258 EPSRC Engineering and Physical Sciences Research Council (20-03-2022 - 19-09-2025)
UK Network on Hyperbolic Equations and related topics - GRANT TRANSFERClaudia Garetto
£1,000 London Mathematical Society (LMS) (01-01-2022 - 30-09-2023)