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Isao SAUZEDDE

Post-doctoral student at Oxford
email: firstname.lastname@maths.ox.ac.uk
Office N101
Mathematical Institute, University of Oxford
Radcliffe Observatory Quarter, Woodstock Road
Oxford OX2 6GG


key-words: planar Brownian motion, winding, intersection measure , Green's formula, rough paths, Riemannian geometry, Yang-Mills theory, Multiplicative chaos


I am currently in post-doc, supervised by Jon Keating. I have just finished (but not defended yet) my PhD at the LPSM (in Paris), under the supervision of Thierry Lévy.

I have been conducting research to study the windings of the planar Brownian motion. By Green's formula, the windings of a curve around the points of a Poisson process in the plane are related to integrals of 1-forms along the curve. It allows for a new definition of some classical integration theories (Young and Stratonovich integrations). Here is a self-contained short presentation of my work (dated from May 2021). You may also take a look at my research statement (dated from March 2021), or at my PhD thesis .


     
My papers:

Lévy area without approximation ArXiv (2021)
Planar Brownian motion winds evenly along its trajectory ArXiv (2021)
Winding and intersection of Brownian motions ArXiv (2021)

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)




My CV