Massimiliano Gubinelli - Stochastic analysis of Euclidean quantum fields

Professor Massimiliano Gubinelli

Stochastic analysis of Euclidean quantum field

Abstract: Stochastic analysis is born when people like Levy, Ito, Doob tried to imagine the paths of continuous Markov processes. It resulted in a beautiful theory at the crossroad of analysis and probability. Later on mathematical physicists, motivated by the study of quantum field theories, started to study more complex random functions than one dimensional diffusions and called them Euclidean quantum fields. These objects resulted much more difficult to understand than Brownian motions and its friends and a lot of mathematics had to be constructed to attack the problem. A recent trend of research is the extension of the basic ideas of stochastic analysis to this (relative) new world. In this talk I will try to describe this line of research and especially the work done in my group to construct these new tools.