Products of (random) distributions in Stochastic PDEs and Quantum Field Theories - Lorenzo Zambotti

Abstract:

 It is well known in mathematical analysis that the pointwise product of functions does not have a canonical extension to the product of Schwartz distributions (also known as generalized functions).  Still, Quantum Field Theory and Stochastic Analysis naturally exhibit examples of non-linear partial differential equations whose solutions are expected to be distributions, and these equations are therefore ill-defined. The last fifteen years there has been impressive progress on these questions, mainly thanks to the work of Martin Hairer and Massimiliano Gubinelli. My aim is to present some of the main ideas underlying this research area, which spans beautifully across many areas in mathematics (analysis, probability, mathematical physics, algebra and geometry).

Bio:

Lorenzo Zambotti is professor at Sorbonne Université in Paris, France. He is there a member of the Laboratoire de Probabilités, Statistique et Modèlisation, of which he has been the director in the period 2020-2024. His research interests include stochastic (partial) differential equations, regularity structures, rough paths, random polymers, large deviations, heat conduction models, neural complexity. He is editor in chief of the journal "Probability Theory and Related Fields". Lorenzo graduated in 1996 from the University of Pisa, with recognition from the Scuola Normale Superiore. There he also received his PhD in 2001. His thesis was supervised by G. Da Prato and was titled "A stochastic parabolic obstacle problem".

Programma completo dell’evento:

14:00 - 15:00: Colloquium Matematico (A102)   

15:00 - 15:50: Rinfresco (Acquario)

16:00 - 16:45: Q&A session "Mathematics: joy and torment (croce e delizia)" (A102)