Paolo graduated in 2017 at the Università di Pisa (with a thesis on stochastic models for the human brain. He has then moved to the University of Warwick where he was a member of the MASDOC CDT programme. After completing the first year with an MSc, he moved to Bath to pursue his PhD. His work concentrates on stochastic particle system models and their convergence to stochastic partial differential equations; particularly, he is very interested in questions of regularity and well-posedness for SPDEs as well as the way the limit equations arises from the particle system. Outside of mathematics, Paolo loves running and cycling, regularly taking part in athletics competitions. He is also often in search for good food and he likes cinemas and theatres.

Research project title:
Convergence of the three-dimensional Ising-Kac model to Φ 34

Supervisor(s):
Hendrik Weber

Project description:
The Ising model is a classical particle system model in statistical physics, where interaction among particles happens at a nearest-neighbour level. If this interaction becomes “mesoscopic”, for example by introducing a radius of interaction which is longer than the microscopic scale and smaller than the macroscopic one, it is possible to prove convergence of the solution to the ϕ4 stochastic differential equation in the two-dimensional torus. The three-dimensional problem poses new challenges, due to the higher irregularity of the noise and to the arising difficulty in defining the limit equation itself. As such, this problem requires the use of recent new powerful techniques like the theory of Regularity Structures. In his PhD, Paolo is focusing on building a framework which makes it possible to treat the discrete particle system in the three-dimensional torus and to prove its convergence to the Φ 34 stochastic differential equation.