Invariant Gibbs measures for the three-dimensional cubic nonlinear wave equation: Part II.

In the two talks, we discuss the proof of invariance of the Gibbs measures for the three- dimensional cubic nonlinear wave equation, which is also known as the hyperbolic Φ4 3- model. In the beginning of the first talk, we briefly review properties of Hamiltonian ODEs, which serve as a toy-model. Then, we state our main theorem and connect it with recent developments in constructive quantum field theory, dispersive PDEs, and stochastic PDEs. In the later parts of the first talk and all of the second talk, we discuss aspects of our proof. In particular, we discuss multilinear dispersive estimates, random operator bounds, and a hidden cancellation. During this discussion, we illustrate the main ideas through simple examples, which should make it accessible to participants with no background in dispersive equations or stochastic PDEs. This is joint work with Y. Deng, A. Nahmod, and H. Yue.