##### Department of Mathematics,

University of California San Diego

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### Math 248 - Analysis Seminar

## Bjoern Bringmann

#### IAS

## Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity

##### Abstract:

In this talk, we discuss the construction and invariance of the Gibbs measure for a three-dimensional wave equation with a Hartree-nonlinearity. In the first part of the talk, we construct the Gibbs measure and examine its properties. We discuss the mutual singularity of the Gibbs measure and the so-called Gaussian free field. In contrast, the Gibbs measure for one or two-dimensional wave equations is absolutely continuous with respect to the Gaussian free field. In the second part of the talk, we discuss the probabilistic well-posedness of the corresponding nonlinear wave equation, which is needed in the proof of invariance. This was the first theorem proving the invariance of a singular Gibbs measure for any dispersive equation.

### November 9, 2021

### 10:00 AM

### https://ucsd.zoom.us/j/99515535778

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