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Seminar Talk

Analysis and PDE

Speaker: Son Tu, MSU
Title: Regularity and Vanishing Viscosity Rates in the Ergodic Problem
When: Wednesday, October 16, 4:00 PM - 4:50 PM
Where: C514 Wells Hall
Contact: Brent Nelson (banelson@msu.edu)
The ergodic problem arises in several key areas of mathematics, including optimal control, homogenization, and classical mechanics. In this talk, I will explore its connections to homogenization, optimal control, and weak KAM (or Aubry-Mather) theory within the framework of Hamilton-Jacobi equations. By applying a stochastic version of weak KAM theory and a technique developed for the domain perturbation problem, we derive explicit formulas for the derivatives of the ergodic constant map (or effective Hamiltonian). This leads to an improved convergence rate for the vanishing viscosity limit (semi-classical limit) under uniform convexity, achieving $O(\varepsilon)$ compared to the previously known $O(\varepsilon^{1/2})$ rate in the literature.