

Abstract for the talk on 09.06.2022 (17:00 h)
Webinar “Analysis, Quantum Fields, and Probability”Bjoern Bringmann (IAS Princeton)
Invariant Gibbs measures for the three-dimensional cubic nonlinear wave equation
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 Φ4 3-
model. This result is
the hyperbolic counterpart to seminal works on the parabolic Φ4 3-
model by Hairer ’14 and Hairer-
Matetski ’18.
In the first 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 first introduce a caloric representation of the Gibbs measure, which leads to an inter-
play of both parabolic and hyperbolic theories. Then, we briefly discuss the local dynamics of the
cubic nonlinear wave equation, focusing on a hidden cancellation between sextic stochastic objects.
This is joint work with Y. Deng, A. Nahmod, and H. Yue.
Webinar links and passwords and program updates will be distributed via email. If you would like to be added to the mailing list, please sign up for the mailing list at lists.uni-leipzig.de/mailman/listinfo/aqfp_announcements.