Isao SAUZEDDE

Research fellow, 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),
EQFT, Higgs-Yang-Mills field, Gaussian free field and log-correlated fields in general, Brownian loop soup, multiplicative chaoses and LQG, SLE, SPDE.
Outside probability theory : Mathematical physics (in particular related to fields theory), Riemannian geometry (in particular stochastic approaches to index theory , e.g. Gauss-Bonnet theorem for the Euler characteristics, 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.
I was previously in post-doc supervised by Jon Keating, after I finished my PhD in Paris (LPSM) supervised by Thierry Lévy.
Recently I was for a few months at the university of Vienna, visiting Nathanael Berestycki. From time to time I am also visiting the university of Luxembourg, visiting Pierre Perruchaud.

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 directly in the continuum the measure associated with Higgs-Yang-Mills field, i.e. a GFF interacting with a Yang-Mills field. Here is a self-contained short presentation of my work (dated from May 2021).

Picture of Brownian windings, showing their fractal structure.

My papers: Most recent: • Renormalised Amperean area of Brownian loops and Symanzik representation of the 2D Higgs-Yang-Mills Fields PDF On Brownian windings: (general theory) •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) (model specific) •Integration and stochastic integration in Gaussian multiplicative chaos. ArXiv (2021) • Homotopy and holonomy of the planar Brownian motion in a Poisson punctured plane. published version (Communications in Mathematical Physics, 2024) ArXiv (2021) Other: • Joint with J.Forkel: Convergence of the logarithm of the characteristic polynomial of unitary Brownian motion in Sobolev space. published version (Journal of Physics A: Mathematical and Theoretical,2024) ArXiv (2022) • Joint with P.Perruchaud: Loop soup representation of zeta-regularised determinants and equivariant Symanzik identities. ArXiv (2024)