Research

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, both in flat and in curved space.

Research interests

– Spectral theory of differential, pseudodifferential and Fourier integral operators
– 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

Publications and preprints

[ArXiv list | Google Scholar]

  1. F. Bambozzi, M. Capoferri, S. Murro:
    Noncommutative Gelfand duality: the algebraic case
    arXiv:2411.11816 [math.AG], 2024 (64 pages). arXiv
  2. M. Capoferri, M. Cherdantsev, I. Velčić:
    High-contrast random systems of PDEs: homogenisation and spectral theory
    arXiv:2312.09046 [math.AP], 2023 (41 pages). arXiv
  3. M. Capoferri, D. Vassiliev:
    Beyond the Hodge Theorem: curl and asymmetric pseudodifferential projections
    arXiv:2309.02015 [math.DG], 2023 (62 pages). arXiv

    Published/accepted papers:
  4. M. Capoferri, S. Murro, G. Schmid
    On boundary conditions for linearised Einstein’s equations
    Applied Mathematics Letters 158 (2024) 109210. Journal arXiv
  5. M. Capoferri, I. Mann:
    Spectral asymptotics for linear elasticity: the case of mixed boundary conditions
    Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, to appear. Journal arXiv
  6. M. Capoferri, S. Murro:
    Global and microlocal aspects of Dirac operators: propagators and Hadamard states
    Advances in Differential Equations, to appear. arXiv
  7. M. Capoferri, M. Cherdantsev, I. Velčić:
    Eigenfunctions localised on a defect in high-contrast random media
    SIAM Journal on Mathematical Analysis 55 6 (2023) 7449-7489. Journal arXiv
  8. M. Capoferri, L. Friedlander, M. Levitin, D. Vassiliev:
    Two-term spectral asymptotic in linear elasticity
    Journal of Geometric Analysis 33 (2023) 242. Journal arXiv
  9. M. Capoferri, G. Rozenblum, N. Saveliev, D. Vassiliev:
    Topological obstructions to the diagonalisation of pseudodifferential systems
    Proceedings of the American Mathematical Society (Ser. B) 9 (2022) 472-486. Journal arXiv
  10. M. Capoferri:
    Diagonalization of elliptic systems via pseudodifferential projections
    Journal of Differential Equations 313 (2022) 157-187. Journal arXiv
  11. Z. Avetisyan, M. Capoferri:
    Partial differential equations and quantum states in curved spacetimes
    Mathematics 9 16 (2021) 1936. Journal
  12. M. Capoferri, D. Vassiliev:
    Invariant subspaces of elliptic systems II: spectral theory,
    Journal of Spectral Theory 12 1 (2022) 301-338. Journal arXiv
  13. M. Capoferri, D. Vassiliev:
    Invariant subspaces of elliptic systems I: pseudodifferential projections
    Journal of Functional Analysis 282 8 (2022) 109402. Journal arXiv
  14. M. Capoferri, D. Vassiliev:
    Global propagator for the massless Dirac operator and spectral asymptotics
    Integral Equations and Operator Theory 94 (2022) 30. Journal arXiv
  15. M. Capoferri, C. Dappiaggi, N. Drago:
    Global wave parametrices on globally hyperbolic spacetimes
    Journal of Mathematical Analysis and Applications 490 (2020) 124316. Journal arXiv
  16. M. Capoferri, M. Levitin, D. Vassiliev:
    Geometric wave propagator on Riemannian manifolds
    Communications in Analysis and Geometry 30 8 (2022) 1713-1777. Journal arXiv
  17. M. Capoferri, N. Saveliev, D. Vassiliev:
    Classification of first order sesquilinear forms
    Reviews in Mathematical Physics 32 (2020) 2050027. Journal arXiv
  18. M. Capoferri, D. Vassiliev:
    Spacetime diffeomorphisms as matter fields
    Journal of Mathematical Physics 61 (2020) 111508. Journal arXiv
  19. M. Benini, M. Capoferri, C. Dappiaggi:
    Hadamard states for quantum Abelian duality,
    Annales Henri Poincaré 18 10 (2017) 3325-3370. Journal arXiv

In preparation:

  • G. Bracchi, M. Capoferri, D. Vassiliev
    Higher order Weyl coefficients for the operator curl
  • M. Capoferri, D. Vassiliev
    A microlocal pathway to spectral asymmetry: curl and the eta invariant
  • B. Costeri, M. Capoferri, C. Dappiaggi
    Spectral asymmetry via pseudodifferential projections: the massless Dirac operator
  • P. Bella, M. Capoferri, M. Cherdantsev, I. Velcic
    Quantitative estimates in high-contrast stochastic homogenisation

Other publications

  1. M. Capoferri, M. Cherdantsev, I. Velčić:
    Homogenisation of the wave equation for long times,
    In: “Arbeitsgemeinschaft: Quantitative Stochastic Homogenization” (A. Gloria and F. Otto Eds.)
    Oberwolfach Reports 48 (2022) 62-64. DOI PDF

Theses