Matteo Capoferri

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.

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

A self-contained description of my research is available upon request.

Publications

[4.]	M. Capoferri, M. Levitin, D. Vassiliev: Geometric wave propagator on Riemannian manifolds arXiv:1902.06982 [math.AP], 2019.
[3.]	M. Capoferri, N. Saveliev, D. Vassiliev: Classification of first order sesquilinear forms arXiv:1811.10318 [math.AP], 2018.
[2.]	M. Capoferri, D. Vassiliev: Spacetime diffeomorphisms as matter fields arXiv:1805.01303 [math-ph], 2018.
[1.]	M. Benini, M. Capoferri, C. Dappiaggi: Hadamard states for quantum Abelian duality, Annales Henri Poincaré 18 10 (2017) 3325-3370.

Theses

Time observable in non-relativistic quantum mechanics
BSc thesis. University of Pavia, July 2014.
The handling of singularities: an introduction to Microlocal Analysis
First level diploma thesis. IUSS Pavia, October 2014.
Algebra of Observables and States for Quantum Abelian Duality
MSc thesis. University of Pavia, July 2016.
A Microlocal-analytic approach to the Propagator of the Wave Operator
IUSS Diploma thesis. IUSS Pavia, May 2017.

Teaching

Regularly updated information about my teaching can be found at the links below:

Academic Year 2019-2020
MATH0042 Mathematical Methods in Chemistry

Academic Year 2018-2019
MATH0042 Mathematical Methods in Chemistry
ME306 Real Analysis (Class Teacher, at LSE)

Academic Year 2017-2018
2017-2018 Teaching Homepage

You are most welcome to send me an email anytime (matteo.capoferri.16 [AT] ucl.ac.uk) with any question you may have.

I have office hours every week during term time (follow the relevant link above); I am also happy to arrange in-person appointment on other days of the week, if I am free.

Talks

7 Nov 2019	Global hyperbolic propagators in curved space, Mathematical Physics Seminar, University of York, UK. (Invited)
30 Sep 2019	The massless Dirac operator: hyperbolic parametrix and spectral asymptotics, Analysis & PDE Seminar, University of Sussex, UK. (Invited)
10 Sep 2019	Global hyperbolic propagators, Workshop on Spectral Geometry and Analysis of Differential Operators, University of Padova, Italy.
4 Jun 2019	Wave propagator on Riemannian manifolds, Mathematics Colloquium, University of Groningen, Netherlands. (Invited)
10 May 2019	Globlal hyperbolic propagators and spectral asymptotics, Junior Analysis Seminar, Imperial College London. (Invited)
4 Mar 2019	Hyperbolic propagators: from scalar equations to first order systems, UK Meeting on Hyperbolic Equations, Loughborough University, United Kingdom. (Invited)
29 Nov 2018	Mathematical encounters of the third kind, Mathematics Undergraduate Colloquium, University College London. (Invited)
5 Nov 2018	Global hyperbolic propagators: a microlocal-analytic approach, Differential geometry seminar, University of Freiburg, Germany. (Invited)
21 Jul 2018	Global hyperbolic propagators in curved space, International Congress of Mathematical Physics, Young Researchers Symposium, Montreal.
6 Jul 2018	Global hyperbolic propagators in curved space, Conference "Microlocal and time-frequency analysis", Turin.
28 Jun 2018	The wave propagator between analysis and geometry, Conference "An analyst, a geometer and a probabilist walk into a bar", Cardiff.
11 Jun 2018	Global hyperbolic propagators in curved space, 10th Birman Conference in Spectral Theory, St Petersburg. (Invited)
5 Jun 2018	Global hyperbolic propagators in curved space, Conference "AQFT: where operator algebra meets microlocal analysis", Cortona, Italy.
30 May 2018	Global hyperbolic propagators in curved space, Mathematical physics seminar, University of Pavia. (Invited)
15 Feb 2018	Solving the wave equation on manifolds, UCL Mathematics PG Seminar.
1 Feb 2018	Hadamard states for Quantum Abelian Duality, 41st LQP Workshop, Mathematisches Institut, Göttingen.
10 Nov 2017	Hyperbolic propagators in curved space, LMS Genearal Meeting - Graduate Student session, London Mathematical Society, London.
28 Aug 2017	Hyperbolic propagator in curved space: an explicit global formula, Conference "Geometric foundations of gravity", Tartu, Estonia.
17 May 2017	The algebraic approach to QFT, UCL Mathematics PG Seminar.

Collaborators

People I am collaborating or have collaborated with:

Dr. Zhirayr Avetisyan (Santa Barbara)
Dr. Federico Bambozzi (Oxford)
Dr. Marco Benini (Hamburg)
Prof. Claudio Dappiaggi (Pavia)
Dr. Nicolò Drago (Trento)
Prof. Michael Levitin (Reading)
Dr. Simone Murro (Freiburg)
Prof. Nikolai Saveliev (Miami)
Dr. Marcello Seri (Groningen)
Prof. Dmitri Vassiliev (UCL)

Useful links

UCL Maths Department
London Analysis Seminar
King's Analysis Seminar
Conferences in Spectral Theory and Mathematical Physics