Isao SAUZEDDE

Post-doctoral student, university of Warwick
email: firstname.lastname@warwick.ac.uk



Specific interests in probability : Brownian motion in dimension 2 to 4 (in particular Brownian windings, stochastic Green' formula, Brownian motion interacting with random magnetic impurities, intersection measure),
Gaussian free field and log-correlated fields in general, Brownian loop soup, multiplicative chaoses, Yang-Mills field, SLE, SPDE
Outside probability theory : Mathematical physics (in particular related to fields theory), Riemannian geometry (in particular geometric and stochastic expressions of topological invariants, e.g. Euler characteristics and analytic torsion, and measures on moduli spaces), Rough path theory
I am currently a post-doc at the university of Warwick, supervised by Aleksandar Mijatović (Although I am currently visiting Nathanael Berestycki at the university of Vienna until the end of 2023). I was previously in post-doc supervised by Jon Keating, after I finished my PhD in Paris (LPSM) supervised by Thierry Lévy.

My research is mostly about the winding function associated with a planar Brownian motion, which can be seen as a sort of log-correlated field. My initial motivation comes from relations with Yang-Mills field, and in particular with the goal of defining in the continuum the measure associated with a GFF interacting with a Yang-Mills field. Here is a self-contained short presentation of my work (dated from May 2021).

Here is a picture I made about Brownian windings,to depicte there fractal structure.

My PhD thesis My papers: On the general theory of Brownian windings: Lévy area without approximation. published version (Annales de l'IHP, 2022) ArXiv (2021) Planar Brownian motion winds evenly along its trajectory. published version (ALEA, 2023) ArXiv (2021) Winding and intersection of Brownian motions. ArXiv (2021) Brownian windings, Stochastic Green's formula and inhomogeneous magnetic impurities. ArXiv (2023) Applications of Brownian windings: Integration and stochastic integration in Gaussian multiplicative chaos. ArXiv (2021) Homotopy and holonomy of the planar Brownian motion in a Poisson punctured plane. ArXiv (2021) Other: Convergence of the logarithm of the characteristic polynomial of unitary Brownian motion in Sobolev space. (Joint work with Johannes Forkel. To appear on Journal of Physics A: Mathematical and Theoretical) ArXiv (2022) My CV