What's Happening in Fine Hall

This talk provides an accessible introduction to probabilistic aspects of nonlinear evolution equations. Research in this area sits at the interface of partial differential equations and probability theory, linking it to several elegant mathematical topics. 

In the first part of this talk, we review Hamiltonian equations, which are ordinary differential equations. Furthermore, we explain how basic results for Hamiltonian equations serve as a motivation for intricate questions on nonlinear wave equations. In the second part, I will present a theorem for the three-dimensional cubic wave equation, obtained in collaboration with Y. Deng, A. Nahmod, and H. Yue. As part of this, we will explore how randomness in the initial data can lead to well-posedness, even in cases where deterministic methods are inapplicable.