Quasi-invariant gaussian measures for the nonlinear wave equation

Nikolay Tzvetkov
Univ. de Cergy-Pontoise

Abstract: We will show that a natural class of gaussian measures living on Sobolev spaces of varying regularity are quasi-invariant under the flow of the two dimensional cubic defocusing wave equation. For that purpose, we introduce renormalised energies and we establish the associated energy estimates.
This is a joint work with Tadahiro Oh (Edinburgh University).

Recent Advances in Kinetic Theory and their connection to Nonlinear PDEs, Functional Inequalities and Applied Probability

Amit Einav
University of Cambridge

Abstract: Kinetic theory is the field of mathematics that deals with systems of many objects. In recent years, this field has seen an awakening and renewed interest, and has been the focus of attention of many prominent mathematicians. In this talk we will discuss recent advances in the field, mainly in relation to the Boltzmann-Nordheim equation and Kac’s Model, and tie them to the fields of Nonlinear PDEs, Functional Inequalities and Applied Probability.