Ergodic Theory of the Stochastic Burgers Equation

Explore the ergodic theory of the stochastic Burgers equation in this comprehensive lecture by Yuri Bakhtin from New York University. Delivered as part of the Colloque des sciences mathématiques du Québec/CSMQ, delve into the study of stationary distributions for the Burgers equation with random forcing. Begin with an examination of a simplified random dynamical system to demonstrate the effectiveness of the pullback procedure. Progress to the analysis of the Burgers equation, a fundamental evolutionary stochastic PDE related to fluid dynamics, growth models, and the KPZ equation. Discover how this approach can be implemented through the study of long-term properties of random Lagrangian action minimizers and directed polymer measures in random environments. Learn about the developments in the compact space case from the 2000s and explore Bakhtin's recent work on the noncompact case, conducted in collaboration with Eric Cator, Kostya Khanin, and Liying Li.