About me

I have been at King's College London since 2022, where I am also a member of the London School of Geometry and Number Theory. Before that, I have been a Research Associate at the University of Bristol, hosted by Asma Hassannezhad, and a Research Fellow at University College London, working with Leonid Parnovski and Alexander Sobolev. I obtained my Ph. D. at Université de Montréal in 2018, under the supervision of Iosif Polterovich. My interests are in asymptotic analysis, mainly in the fields of spectral geometry, elliptic PDEs, homogenisation theory, geometric analysis and the geometry of numbers. I am more specifically interested in situations where there are more than one asymptotic parameter, and how their relations affect the behaviour of the problem. The following type of questions are of particular interest to me.

  • Consider a sequence of domains perforated with smaller and smaller holes distributed uniformly inside, a process known as homogenisation. What is the behaviour of boundary spectral problems, such as the Steklov problem, in this limit? Can we use this to make links between different eigenvalue problems?
  • Can we describe the spectrum of a periodic, quasi-periodic or almost-periodic operator in the presence of resonators, or in very thin media?
  • Given a sequence of optimisers for the kth eigenvalue of an elliptic operator, can we ensure that this sequence converges in any meaningful sense to a limit object?
  • Given an anisotropically expanding convex domain, under what conditions on this anisotropicity can we meaningfully count the number of lattice points contained inside.
To answer these questions, I use tools from operator theory, classical PDEs, harmonic analysis, calculus of variations and analytic number theory. I am not currently recruiting PhD students. If you are interested in applyign for a postdoctoral fellowship hosted at King's College London, you can contact me.

Seminars

I organise a few seminars:

  • The Spectral Geometry in the Clouds seminar , that meets online every Monday at 16GMT (with some exceptions).
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  • The London Analysis and Probability Seminar, that meets during term time more or less every other Thursday at 15 for two seminars. The sessions rotate between UCL in autumn, Imperial College in winter and King's College in Spring.
    To join the maling list, please follow instructions here, and refer to the website for precise dates and locations.
  • The King's Analysis seminar, that meets during term time every Thursday at 11 in the Strand Building of King's College London.
    To join the mailing list please email me.

Research

    Preprints

  1. Canonical Foliations of Bubblesheets (with Stephen Lynch ).
    arXiv:2411.14340
  2. Spectral decomposition and Siegel–Veech transforms for strata: The case of marked tori (with Jayadev S. Athreya , Martin Möller and Martin Raum ).
    arXiv:2404.06597.
  3. Sharp density discrepancy for cut and project sets: An approach via lattice point counting. (with Henna Koivusalo , and an appendix by Michael Björklund and Tobias Hartnick ).
    arXiv:2401.01803

    4. Published papers

  4. Flexibility of Steklov eigenvalues via boundary homogenisation (with Mikhail Karpukhin ),
    Annales Mathématiques du Québec 48 (2024)
  5. Weyl's law for the Steklov problem on surfaces with rough boundary (with Mikhail Karpukhin and Iosif Polterovich ).
    Archive for Rational Mechanics and Analysis 247:5 (2023).
  6. Homogenisation as control: mimicking eigenvalue problems.
    Oberwolfach Reports 36 (2023), pp. 2088–2091.
  7. The almost periodic gauge transform: an abstract scheme with applications to Dirac operators (with Sergey Morozov , Leonid Parnovski , Bernhard Pfirsch, and Roman Shterenberg ).
    Annales Henri Lebesgue 6 (2023)
  8. Spectral invariants of Dirichlet-to-Neumann operators on surfaces (with Simon St-Amant ).
    Journal of Spectral Theory 11:4 (2021).
  9. Large Steklov eigenvalues via homogenisation on manifolds (with Alexandre Girouard ).
    Inventiones Mathematicae 226 (2021)
  10. Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems (with Mikhail Karpukhin and Alexandre Girouard ).
    Geometric and Functional Analysis (GAFA) 31 (2021)
  11. Optimal unions of scaled copies of domains and Pólya's conjecture (with Pedro Freitas and Jordan Payette).
    Arkiv för Matematik 59 (2021)
  12. From Steklov to Neumann via Homogenisation (with Alexandre Girouard and Antoine Henrot ).
    Archive for Rational Mechanics and Analysis 239:2 (2021)
  13. Eigenvalue optimisation on flat tori and lattice points in anisotropically expanding domains.
    Canadian Journal of Mathematics 72:4 (2020)
  14. The Steklov spectrum of cuboids(with Alexandre Girouard , Iosif Polterovich , and Alessandro Savo ).
    Mathematika 65:2 (2019)
  15. A generalised Gauss circle problem and integrated density of states (with Leonid Parnovski ).
    Journal of Spectral Theory 6:4 (2016)

    16. Thesis

Other organisations

The following pages may be useful to anyone interested in spectral geometry.