Title: Hitting probabilities and capacity for SPDEs

Abstract: In this talk we are interested in one of the basic problems of potential theory for stochastic processes, which is the following:

when does a stochastic process hit a given set with positive probability ? Sets that are never visited by the process are said to be polar,

otherwise they are non-polar. Probabilistic potential theory gives a way to compute this probabilistic quantity in terms of an analytic

function named the capacity of the set that will depend on the process. We will first give a resume of the existing results in the literature

and the techniques used to solve this problem for different stochastic processes, such as the Brownian motion and more general Gaussian processes.

We will then explain how to solve this problem for processes that are solutions to different stochastic partial differential equations (SPDEs),

such as the non-linear wave and heat equation perturbed by a Gaussian noise.