Seminar

Diffuse domain methods (DDMs) have attracted significant attention for approximating solutions to partial differential equations on complex geometries in two and three dimensions. These methods implicitly represent the geometry by replacing the sharp boundary interface with a diffuse layer of thickness $\epsilon$. We will define and consider both one-sided and two-sided versions of the problem. For the one-sided case, this approach reformulates the original equations on an extended, regular domain (for example, a hyper-cuboid).

Abstract: We will continue talking about motivic classes. We will first review the motivic classes of varieties. Then we will focus on the motivic classes of stacks. In particular, we will give the explicit formulas for the motivic classes of moduli of Higgs bundles and bundles with connections.