In this page you can find my papers and theses.

Research

Stability of the Faber-Krahn inequality for the short-time Fourier transform

We prove a sharp quantitative version of the Faber-Krahn inequality for the short-time Fourier transform.
with A. Guerra, J. P. G. Ramos, P. Tilli,
Inventiones Mathematicae, (2024).

Theses

Bachelor's

This is my bachelor's thesis. It shows results for Hausdorff dimension of self-similar sets, the relation between Hausdorff dimension and the Fourier transform and an application to a distance set problem in geometric measure theory. (ES)

Master's

This is my master's thesis. We show the sharp quantitative Faber-Krahn inequality for the short-time Fourier transform and a wavelet analogue result.

Semester Papers

Stability of Isoperimetric Inequalities

We study the stability of the classical and anisotropic isoperimetric inequalities in the Euclidean space, as shown in the papers by N. Fusco, F. Maggi and A. Pratelli, and A. Figalli, F. Maggi and A. Pratelli.

The Faber-Krahn inequality for the STFT

We provide the details and preliminaries of a recent paper by F. Nicola and P. Tilli showing an analogue of the Faber-Krahn inequality in the context of time-frequency analysis.