Analysis Seminar

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Quantitative homogenization in high contrast

Speaker: Tuomo Kuusi, University of Helsinki

Location: Warren Weaver Hall 1302

Date: Thursday, February 15, 2024, 11 a.m.

Synopsis:

There is a relatively complete theory of quantitative homogenization for uniformly elliptic equations in the regime of "moderate” ellipticity contrast,  meaning that the estimates depend implicitly on the ellipticity ratio. The "high contrast" regime, on the other hand, is wide open. I will discuss some recent and ongoing work on extending the theory to the regime of high contrast. In the process, we manage to develop an exact renormalization procedure, which is expected to have applications in mathematical physics beyond the setting of elliptic homogenization. Time permitting I will discuss some of these applications.