# Bjoern Bringmann, IAS – Analysis & PDE Seminar

## August 31 @ 3:00 pm - 4:00 pm

**Speaker:** Bjoern Bringmann.

**Title:** Invariant Gibbs measures for the three-dimensional cubic nonlinear wave equation.

**Abstract:** In this talk, we prove the invariance of the Gibbs measure for the three-dimensional cubic nonlinear wave equation, which is also known as the hyperbolic Φ43-model. This result is the hyperbolic counterpart to seminal works on the parabolic Φ43-model by Hairer ’14 and Hairer-Matetski ’18.

In the rst half of this talk, we illustrate Gibbs measures in the context of Hamiltonian ODEs, which serve as toy-models. We also connect our theorem with classical and recent developments in constructive QFT, dispersive PDEs, and stochastic PDEs.

In the second half of this talk, we give a non-technical overview of the proof. As part of this overview, we rst introduce a caloric representation of the Gibbs measure, which leads to an interplay of both parabolic and hyperbolic theories. Then, we discuss our para-controlled Ansatz and a hidden cancellation between sextic stochastic objects.

This is joint work with Y. Deng, A. Nahmod, and H. Yue.