Professor of Mathematics
Science and Engineering EDI Lead and Deputy Head of School
Hyperbolic equations, Low regular coefficients, Multiplicities, Generalised Solutions, Fourier Analysis, Mathematical Analysis
Publications of specific relevance to the Centre for Geometry, Analysis and GravitationSchwartz very weak solutions for Schrödinger type equations with distributional coefficientsSchrödinger type equations with singular coefficients and lower order termsC∞ Well-Posedness of Higher Order Hyperbolic Pseudo-Differential Equations with Multiplicities
Schwartz very weak solutions for Schrödinger type equations with distributional coefficients$C^\infty$ well-posedness of higher order hyperbolic pseudo-differential equations with multiplicitiesDiversifying the STEM curriculumSchrödinger type equations with singular coefficients and lower order termsHyperbolic systems with non-diagonalisable principal part and variable multiplicities, III: singular coefficientsOn Hyperbolic Equations with Space-Dependent Coefficients: C∞ Well-Posedness and Levi ConditionsOn the Wave Equation with Space Dependent Coefficients: Singularities and Lower Order TermsOn the wave equation with space dependent coefficients: singularities and lower order termsInhomogeneous wave equation with t-dependent singular coefficientsInhomogeneous wave equation with $t$-dependent singular coefficientsOn the wave equation with multiplicities and space-dependent irregular coefficientsHyperbolic systems with non-diagonalisable principal part and variable
multiplicities, II: microlocal analysisHyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: microlocal analysisHyperbolic systems with non-diagonalisable principal part and variable multiplicities, I: well-posednessHyperbolic systems with non-diagonalisable principal part and variable multiplicities, I. Well-posednessOn C∞ well-posedness of hyperbolic systems with multiplicitiesWell-posedness of hyperbolic systems with multiplicities and smooth coefficientsWell-posedness of hyperbolic systems with multiplicities and smooth coefficientsOn hyperbolic systems with time-dependent Hölder characteristicsOn $C^\infty$ well-posedness of hyperbolic systems with multiplicitiesOn hyperbolic equations and systems with non-regular time dependent coefficientsOn hyperbolic systems with time dependent Hölder characteristicsWave equation for sums of squares on compact Lie groupsHyperbolic Second Order Equations with Non-Regular Time Dependent CoefficientsSymmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficientsA note on weakly hyperbolic equations with analytic principal partWave equation for sums of squares on compact Lie groupsHyperbolic second order equations with non-regular time dependent coefficientsGeneralized Fourier Integral Operator Methods for Hyperbolic Equations with SingularitiesWeakly hyperbolic equations with non-analytic coefficients and lower order termsOn weakly hyperbolic equations with analytic principal partOn the well-posedness of weakly hyperbolic equations with time dependent coefficientsOn the well-posedness of weakly hyperbolic equations with time-dependent coefficientsWeakly hyperbolic equations with non-analytic coefficients and lower order termsLp and Sobolev boundedness of pseudodifferential operators with non-regular symbol: A regularisation approachSymmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficientsGeneralised Fourier integral operator methods for hyperbolic equations with singularitiesHilbert C ~ \widetilde {\mathbb {C}} -modules: Structural properties and applications to variational problemsSufficient conditions of local solvability for partial differential operators on spaces of colombeau typeClosed graph and open mapping theorems for topological $ \tilde \lc $‐modules and applicationsGeneralized oscillatory integrals and Fourier integral operatorsFundamental Solutions in the Colombeau Framework: Applications to Solvability and Regularity TheoryGeneralized Fourier Integral Operators on Spaces of Colombeau TypeHilbert $\widetilde{\C}$-modules: structural properties and applications to variational problemsMicrolocal analysis in the dual of a Colombeau algebra: Generalized wave front sets and noncharacteristic regularityGeneralized Oscillatory Integrals and Fourier Integral OperatorsOn duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front setsTopological Structures in Colombeau Algebras: Investigation of the Duals of , andPseudodifferential operators with generalized symbols and regularity theoryMICROLOCAL ANALYSIS OF GENERALIZED FUNCTIONS: PSEUDODIFFERENTIAL TECHNIQUES AND PROPAGATION OF SINGULARITIESTopological Structures in Colombeau Algebras: Topological -modules and Duality TheoryOn duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front setsMicrolocal analysis of generalized functions: pseudodifferential techniques and propagation of singularitiesPseudo-Differential Operators in Algebras of Generalized Functions and Global HypoellipticityGrants of specific relevance to the Centre for Geometry, Analysis and GravitationHyperbolic problems with discontinuous coefficients-GRANT TRANSFERUK Network on Hyperbolic Equations and related topics - GRANT TRANSFERQMUL has joined the Einstein Telescope (ET) collaboration with a new ET Research Unit supported by School of Mathematical Sciences and the School of Physical and Chemical Sciences. ET is a European project, driven by an international collaboration, for an innovative gravitational-wave observatory. It will be part of a third-generation ... [more]
Many congratultons to Claudia Garetto who has been awarded the 2026 Suffrage Science Award for Maths and Computing, a prestigious peer-to-peer award recognising outstanding women in science for both research excellence and their commitment to inspiring others. The Suffrage Science Awards are unique in their format and ethos: each recipient nominates ... [more]
