Dr Matteo Capoferri

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

Publications and preprints

Preprints:

[13.] M. Capoferri, G. Rozenblum, N. Saveliev, D. Vassiliev
Topological obstructions to the diagonalisation of pseudodifferential systems
arXiv:2203.16957 [math.AP], 2022 (15 pages).

[12.] M. Capoferri, S. Murro
Global and microlocal aspects of Dirac operators: propagators and Hadamard states
arXiv:2201.12104 [math.AP], 2022 (40 pages).

[11.] M. Capoferri, M. Cherdantsev, I. Velčić
Eigenfunctions localised on a defect in high-contrast random media
arXiv:2104.02674 [math.SP], 2021 (40 pages).

[10.] M. Capoferri, D. Vassiliev
Global propagator for the massless Dirac operator and spectral asymptotics
arXiv:2004.06351 [math.AP], 2020 (50 pages).

Publications:

[9.] M. Capoferri
Diagonalization of elliptic systems via pseudodifferential projections
Journal of Differential Equations 313 (2022) 157-187.

[8.] Z. Avetisyan, M. Capoferri
Partial differential equations and quantum states in curved spacetimes
Mathematics 9 16 (2021) 1936.

[7.] M. Capoferri, D. Vassiliev
Invariant subspaces of elliptic systems II: spectral theory
Journal of Spectral Theory 12 1 (2022) 301-338.

[6.] M. Capoferri, D. Vassiliev
Invariant subspaces of elliptic systems I: pseudodifferential projections
Journal of Functional Analysis 282 8 (2022) 109402.

[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
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:

• M. Capoferri, D. Vassiliev
  Beyond the Hodge Theorem: curl and asymmetric pseudodifferential projections.
  
• M. Capoferri, M. Cherdantsev, I. Velcic
  High-contrast random systems of PDEs: homogenisation and spectral theory.
• M. Capoferri, L. Friedlander, M. Levitin, D. Vassiliev
  Two-term spectral asymptotics for linear elasticity.
• 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)

Past projects