Dr Matteo Capoferri
Research Associate
- capoferrim@cardiff.ac.uk
- +44 (0)29 2087 0617
- Room M/2.44, Maths and Education Building , Senghennydd Road, Cardiff, CF24 4AG
Overview
My area of research expertise is, broadly speaking, the analysis of partial differential equations (PDEs). More specifically, the microlocal and spectral analysis of differential, pseudodifferential and Fourier integral operators on manifolds.
I am a member of the Mathematical Analysis Research Group and my research is funded by the Leverhulme Trust grant "Stochastic homogenisation of high-contrast composites" held by Dr Mikhail Cherdantsev.
Research interests
- Spectral theory of differential, pseudodifferential and Fourier integral operators on manifolds
- Global hyperbolic propagators
- Analysis of first order systems of PDEs (elliptic or hyperbolic)
- Spectral asymptotics and spectral geometry
- Mathematical elasticity
- Spectral problems in the homogenisation of stochastic PDEs
Biography
Education
- 2016 - 2020: PhD in Mathematics, Department of Mathematics, University College London, London, UK
Thesis: Microlocal analysis of global hyperbolic propagators on manifolds without boundary (Supervisor: Prof D. Vassiliev) - 2014 - 2016: MSc in Theoretical Physics, Department of Physics, University of Pavia, Italy
Thesis: Algebra of Observables and States for Quantum Abelian Duality (Supervisors: Prof C. Dappiaggi and Dr M. Benini)
Final mark: 110/110 summa cum laude - 2011 - 2014: BSc in Physics, Department of Physics, University of Pavia, Italy
Thesis: Time observable in non-relativistic quantum mechanics (Supervisor: Prof C. Dappiaggi)
Final mark: 110/110 summa cum laude - 2011 - 2017: University diploma, Class of Sciences and Technologies, Institute for advanced study IUSS, Pavia, Italy
First level thesis: The handling of singularities: an introduction to microlocal analysis (Supervisor: Prof C. Dappiaggi)
Diploma thesis: A microlocal-analytic approach to the propagator of the wave operator (Supervisor: Prof D. Vassiliev) - 2011 - 2016: Fellow, Almo Collegio Borromeo, Pavia, Italy
Honours and awards
- Faculty of Mathematical and Physical Sciences Postgraduate Research Dean’s Commendation, “For the outstanding performance in the PhD in Mathematics“, UCL (2021)
- Clay Mathematics Institute (Conference grant), jointly with C. Garetto and D. Vassiliev (2020)
- LMS Research Grant (Scheme 4) (2020)
- LMS Research Grant (Scheme 1), jointly with C. Garetto and D. Vassiliev (2019)
- MAPS Faculty Teaching Award, UCL (2019)
- Archibald Richardson Scholarship for Pure Mathematics, UCL (2019)
- Sir George Jessel Scholarship, UCL (2018)
- Davenport Prize for Pure Mathematics, UCL (2018)
- Springer Fellowship, Canadian Mathematical Society (2018)
- Grazioli Prize, Istituto Lombardo Accademia di Scienze e Lettere (2018)
- IUSS Scholarship, Institute for Advanced Study, Pavia (2011-2016)
Professional memberships
- London Mathematial Society
- European Mathematical Society
Academic positions
2020 - present: Research associate, Cardiff University
Teaching
I mainly taught mathematical analysis, both to mathematicians and non-mathematicians.
2020/2021
- Teaching Assistant for the course “Spectral theory of Hilbert spaces”, Séminaires de Mathématiques Supérieures 2021 “Microlocal analysis: theory and applications“, CRM, Montreal.
- Lecturer for "An introduction to quantum field theory in curved spacetime” (with D. Siemssen, York), course for PhD students (online delivery). Funded by the London Mathematical Society.
2019/2020
- Lecturer for MATH0042 "Mathematical methods in chemistry", UCL
2018/2019
- Lecturer for MATH0042 "Mathematical methods in chemistry", UCL
- Demonstrator for Analysis 4, UCL
- Class teacher for ME306 "Real analysis", London School of Economics
2017/2018
- Problem class teacher for MATH7102 "Analysis 4", UCL
- Problem class teacher for MATH6106 "Mathematics for Science 2", UCL
- Tutorials in Pure Mathematics (Analysis 1 & 2, Algebra 1 & 2), UCL
- Demonstrator for MATH1101 "Analysis 1" and MATH7102 "Analysis 4", UCL
2016/2017
- Tutorials in Pure Mathematics (Analysis 1 & 2, Algebra 1 & 2), UCL
- Demonstrator for MATH1101 "Analysis 1" and MATH7102 "Analysis 4", UCL
2015/2016
- Problem class teacher for "General Mathematics" for Economics students, University of Pavia
- Tutorials for the course "General Mathematics" for Economics students, University of Pavia
- Teaching assistant for the course for the course "Experimental Physics with Laboratory" (4 didactic seminars on Thermodynamics and Introductory Quantum Mechanics), University of Pavia
Publications and preprints
[9.] M. Capoferri, M. Cherdantsev, I. Velčić
Eigenfunctions localised on a defect in high-contrast random media
arXiv:2104.02674 [math.SP], 2021 (40 pages).
[8.] M. Capoferri, D. Vassiliev
Invariant subspaces of elliptic subspaces of elliptic systems II: spectral theory
arXiv:2103.14334 [math.AP], 2021 (33 pages).
[7.] M. Capoferri, D. Vassiliev
Invariant subspaces of elliptic subspaces of elliptic systems I: pseudodifferential projections
arXiv:2103.14325 [math.AP], 2021 (39 pages).
[6.] M. Capoferri, D. Vassiliev
Global propagator for the massless Dirac operator and spectral asymptotics
arXiv:2004.06351 [math.AP], 2020 (50 pages).
[5.] M. Capoferri, C. Dappiaggi, N. Drago
Global wave parametrices on globally hyperbolic spacetimes
Journal of Mathematical Analysis and Applications 490 no. 2 (2020) 124316.
[4.] M. Capoferri, M. Levitin, D. Vassiliev
Geometric wave propagator on Riemannian manifolds
arXiv:1902.06982 [math.AP], 2019 (43 pages),
to appear in Communications in Analysis and Geometry.
[3.] M. Capoferri, N. Saveliev, D. Vassiliev
Classification of first order sesquilinear forms
Reviews in Mathematical Physics 32 (2020) 2050027.
[2.] M. Capoferri, D. Vassiliev
Spacetime diffeomorphisms as matter fields
Journal of Mathematical Physics 61 (2020) 111508.
[1.] M. Benini, M. Capoferri, C. Dappiaggi
Hadamard states for quantum Abelian duality,
Annales Henri Poincaré 18 10 (2017) 3325-3370.
In preparation:
F. Bambozzi, M. Capoferri, S. Murro
The geometry of formal deformation quantization.
Supervision
- Co-supervision (with D. Vassiliev) of the summer project of Ziqi Wang, UCL (2019)