Skip to main content
Dr Matteo Capoferri

Dr Matteo Capoferri

Research Associate

School of Mathematics

Email
capoferrim@cardiff.ac.uk
Telephone
+44 (0)29 2087 0617
Campuses
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

[10.] M. Capoferri
Diagonalization of elliptic systems via pseudodifferential projections
arXiv:2106.07948 [math.AP], 2021 (29 pages).

[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 systems II: spectral theory
arXiv:2103.14334 [math.AP], 2021 (33 pages),
to appear in Journal of Spectral Theory.

[7.] M. Capoferri, D. Vassiliev
Invariant 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)

Areas of expertise

External profiles