2026 SPRING ABSTRACTS

Jan 20 @ Penn: Aidan Lau (NYU) 

Stochastic homogenization of coarse-grained elliptic equations

In stochastic homogenization, solutions to a heterogeneous equation converge to the solution to a homogeneous equation provided that the coefficients are stationary, ergodic and satisfy a sufficient ellipticity condition. I will explain why certain coarse-grained ellipticity constants appear naturally in homogenization, show that boundedness of the coarse-grained ellipticity constants implies quenched homogenization of the PDE, and compare this to recent results on the random conductance model and the case of a divergence-free drift.