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Bjoern Bringmann, IAS – Analysis & PDE Seminar
August 31, 2022 @ 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.