About me

Since January 2022, I am a Lecturer in Pure Mathematics at King’s College London, where I am also a member of the London School in 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.

I am one of the co-organisers of the Spectral Geometry in the Clouds online seminar, along with Alexandre Girouard and Laura Monk. In this seminar, we discuss eveyrhting related to spectral geometry and geometric analysis, and we sometimes delve in hyperbolic geometry, analytic number theory and mathematical physics when the subjects are related. If you are interested in attending, simply write an email to me and I will add you to the mailing list or send you the zoom link.

My interests are in asymptotic analysis, mainly in the fields of spectral geometry, elliptic PDEs, homogenisation theory 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 k’th 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.