I am currently a Ph. D. candidate at Université de Montréal under the supervision of Iosif Polterovich. My interests are in asymptotic analysis, mainly in the fields of spectral theory and of 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.
- 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 harmonic analysis, analytic number theory and microlocal analysis.
I also organise the Montreal seminar in spectral geometry, held weekly at Université de Montréal.