Student Analysis Seminar

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An introduction to homogenization and coarse-grained ellipticity

Speaker: Aidan Lau, NYU Courant

Location: Warren Weaver Hall 201

Date: Monday, March 23, 2026, 12:30 p.m.

Synopsis:

Systems with microscopic disorder display macroscopic order in the limit of large scale separation. This coarse-graining process can be described by the homogenization of (periodic or random) elliptic and parabolic differential operators. I will begin by introducing the basic objects of homogenization (correctors, the effective diffusion matrix and the coarse-grained matrices) and computing a simple example. I will then discuss quantitative homogenization results and give some theorems which illustrate the importance of the coarse-grained ellipticity constants.