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 Gravitation2025
Schrödinger type equations with singular coefficients and lower order termsArias A, Ascanelli A, Cappiello M and Garetto C
Journal of Differential Equations, Elsevier vol. 425, 190-222.
01-04-2025
2024
Diversifying the STEM curriculumShah R, Garetto C, Belafonte AD and Serrano MFP
Queen Mary Festival of Education London, United Kingdom 6 Mar 2024 - 7 Mar 2024.
07-03-2024
Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, III: singular coefficientsGaretto C and Sabitbek B
Mathematische Annalen, Springer
19-01-2024
On Hyperbolic Equations with Space-Dependent Coefficients: C∞ Well-Posedness and Levi ConditionsGaretto C
In Women in Analysis and Pde, Springer Nature 163-173.
01-01-2024
2023
On the Wave Equation with Space Dependent Coefficients: Singularities and Lower Order TermsDiscacciati M, Garetto C and Loizou C
Acta Applicandae Mathematicae, Springer Nature vol. 187 (1), 10-10.
13-09-2023
2022
Inhomogeneous Wave Equation with T-Dependent Singular CoefficientsDiscacciati M, Garetto C and Loizou C
Journal of Differential Equations
02-03-2022
2021
On the wave equation with multiplicities and space-dependent irregular coefficientsGaretto C
Transactions of The American Mathematical Society, American Mathematical Society (Ams) vol. 374 (5), 3131-3176.
12-02-2021
2020
Hyperbolic systems with non-diagonalisable principal part and variable
multiplicities, II: microlocal analysisGaretto C, Jäh C and Ruzhansky M
Journal of Differential Equations, Elsevier
16-06-2020
2018
Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posednessGaretto C, Jäh C and Ruzhansky M
Mathematische Annalen, Springer Nature vol. 372 (3-4), 1597-1629.
22-03-2018
2017
On C∞ well-posedness of hyperbolic systems with multiplicitiesGaretto C and Ruzhansky M
Annali Di Matematica Pura Ed Applicata (1923 -), Springer Nature vol. 196 (5), 1819-1834.
25-02-2017
2016
Well-posedness of hyperbolic systems with multiplicities and smooth coefficientsGaretto C and Jäh C
Mathematische Annalen, Springer Nature vol. 369 (1-2), 441-485.
22-06-2016
On hyperbolic systems with time-dependent Hölder characteristicsGaretto C and Ruzhansky M
Annali Di Matematica Pura Ed Applicata vol. 196 (1), 155-164.
12-04-2016
2015
On hyperbolic equations and systems with non-regular time dependent coefficientsGaretto C
Journal of Differential Equations, Elsevier vol. 259 (11), 5846-5874.
01-12-2015
Wave equation for sums of squares on compact Lie groupsGaretto C and Ruzhansky M
Journal of Differential Equations, Elsevier vol. 258 (12), 4324-4347.
01-06-2015
2014
Hyperbolic Second Order Equations with Non-Regular Time Dependent CoefficientsGaretto C and Ruzhansky M
Archive For Rational Mechanics and Analysis, Springer Nature vol. 217 (1), 113-154.
20-12-2014
Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficientsGaretto C and Oberguggenberger M
Mathematische Nachrichten, Wiley vol. 288 (2-3), 185-205.
17-11-2014
A note on weakly hyperbolic equations with analytic principal partGaretto C and Ruzhansky M
Journal of Mathematical Analysis and Applications, Elsevier vol. 412 (1), 1-14.
01-04-2014
2013
Generalized Fourier Integral Operator Methods for Hyperbolic Equations with SingularitiesGaretto C and Oberguggenberger M
Proceedings of The Edinburgh Mathematical Society, Cambridge University Press (Cup) vol. 57 (2), 426-463.
19-09-2013
Weakly hyperbolic equations with non-analytic coefficients and lower order termsGaretto C and Ruzhansky M
Mathematische Annalen, Springer Nature vol. 357 (2), 401-440.
05-02-2013
2012
On the well-posedness of weakly hyperbolic equations with time-dependent coefficientsGaretto C and Ruzhansky M
Journal of Differential Equations, Elsevier vol. 253 (5), 1317-1340.
01-09-2012
2011
Lp and Sobolev boundedness of pseudodifferential operators with non-regular symbol: A regularisation approachGaretto C
Journal of Mathematical Analysis and Applications, Elsevier vol. 381 (1), 328-343.
01-09-2011
2010
Hilbert C ~ \widetilde {\mathbb {C}} -modules: Structural properties and applications to variational problemsGaretto C and Vernaeve H
Transactions of The American Mathematical Society, American Mathematical Society (Ams) vol. 363 (4), 2047-2090.
02-11-2010
2009
Sufficient conditions of local solvability for partial differential operators on spaces of colombeau typeGaretto C
Electronic Journal of Differential Equations vol. 2009, 1-43.
21-09-2009
Closed graph and open mapping theorems for topological $ \tilde \lc $‐modules and applicationsGaretto C
Mathematische Nachrichten, Wiley vol. 282 (8), 1159-1188.
21-07-2009
Generalized oscillatory integrals and Fourier integral operatorsGaretto C, Hörmann G and Oberguggenberger M
Proceedings of The Edinburgh Mathematical Society, Cambridge University Press (Cup) vol. 52 (2), 351-386.
28-05-2009
2008
Fundamental Solutions in the Colombeau Framework: Applications to Solvability and Regularity TheoryGaretto C
Acta Applicandae Mathematicae, Springer Nature vol. 102 (2-3), 281-318.
08-02-2008
Generalized Fourier Integral Operators on Spaces of Colombeau TypeGaretto C
In New Developments in Pseudo-Differential Operators, Springer Nature 137-184.
01-01-2008
2006
Microlocal analysis in the dual of a Colombeau algebra: Generalized wave front sets and noncharacteristic regularityGaretto C
New York Journal of Mathematics vol. 12, 275-318.
25-09-2006
On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front setsGaretto C and Hormann G
Bulletin Classe Des Sciences Mathematiques Et Natturalles, National Library of Serbia vol. 133 (31), 115-136.
01-01-2006
2005
Topological Structures in Colombeau Algebras: Investigation of the Duals of , andGaretto C
Monatshefte FüR Mathematik, Springer Nature vol. 146 (3), 203-226.
28-10-2005
Pseudodifferential operators with generalized symbols and regularity theoryGaretto C, Gramchev T and Oberguggenberger M
Electronic Journal of Differential Equations vol. 2005
21-10-2005
MICROLOCAL ANALYSIS OF GENERALIZED FUNCTIONS: PSEUDODIFFERENTIAL TECHNIQUES AND PROPAGATION OF SINGULARITIESGaretto C and Hörmann G
Proceedings of The Edinburgh Mathematical Society, Cambridge University Press (Cup) vol. 48 (3), 603-629.
15-09-2005
Topological Structures in Colombeau Algebras: Topological -modules and Duality TheoryGaretto C
Acta Applicandae Mathematicae, Springer Nature vol. 88 (1), 81-123.
01-08-2005
2004
Pseudo-Differential Operators in Algebras of Generalized Functions and Global HypoellipticityGaretto C
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