Videos

Recent Trends in Stochastic Partial Differential Equations: Fermionic stochastic analysis

Presenter
November 17, 2025
Keywords:
  • stochastic partial differential equations
  • regularity structures
  • paracontrolled calculus
  • nonlinear dispersive equations
  • Gibbs measures
  • homogenization
  • stochastic fluid dynamics
  • quantum field theory
MSC:
  • 60H15 - Stochastic partial differential equations (aspects of stochastic analysis)
Abstract
I will talk about stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. The idea of using Grassmann random variables for fermionic systems goes back to Osterwalder and Schrader, and to implement it we used tools from non-commutative analysis. I will describe some of the stochastic analytical tools such as Grassmann Brownian motion and non-​commutative $L^{p}$ spaces, and mention some of the applications and open questions. Based on the joint work with F. De Vecchi, L. Fresta and M. Gubinelli.