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 "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.