Speaker: Tuomo Kuusi
Title: Quantitative homogenization in high contrast
Abstract: There is a relatively complete theory of quantitative homogenization
for uniformly elliptic equations in the regime of "moderateā 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.