Thomas Beretti

I am completing a PhD in mathematical analysis at SISSA, with a focus on harmonic analysis. More precisely, I study how the geometry of a set is encoded in its Fourier transform — for instance, this paper shows that the perimeter of a set is a weighted limit of its spectral energy. The interplay between geometry and Fourier analysis finds applications in discrepancy theory; the latter is a branch of discrete mathematics that quantifies how point distributions in a space deviate from uniformity, and has applications to numerical integration, quasi-Monte Carlo methods, and number theory.

Currently, I am looking into areas of applied mathematics, such as learning theory and time-frequency analysis, and I will be on the job market starting October 2026. At the same time, I am carrying out various AI-assisted projects: given the inevitable paradigm shift that LLMs are bringing to academia and research, I am investing time and resources in learning how to use such technologies proficiently. In particular, this website was built with Claude Code.