Transport of Gaussian measures under the flow of semilinear (S)PDEs: quasi-invariance and singularity

In this talk, we consider the Cauchy problem for a number of semilinear PDEs, subject to initial data distributed according to a family of Gaussian measures.

We first discuss how the flow of Hamiltonian equations transports these Gaussian measures. When the transported measure is absolutely continuous with respect to the initial measure, we say that the initial measure is quasi-invariant.

We will discuss possible applications of quasi-invariance, and explore various techniques to show it.

We will also discuss how the same techniques can be used in the context of stochastic PDEs, and how they provide information on the invariant measures for their flow.

This is based on joint works with J. Coe (University of Edinburgh), J. Forlano (Monash University), and M. Hairer (EPFL).

• Speaker: Leonardo Tolomeo (University of Edinburgh)
• Thursday 12 June 2025, 15:00–16:00
• Venue: Centre for Mathematical Sciences, MR14.
• Series: Applied and Computational Analysis; organiser: Georg Maierhofer.