EVENT DETAILS AND ABSTRACT

Title: Geometric Analysis of Affine Spheres over Polygons
Speaker: Michael Wolf
Speaker Info: Rice University
Brief Description:
Special Note:
Abstract:

The equation defining affine spherical graphs is one of the more studied geometric analysis of PDE, with basic existence, uniqueness, regularity and embeddedness results due to Cheng-Yau, C.P.Wang, Li, Simon, and Trudinger-Wang. We discuss a parametric theory for affine spheres which are conformally planar, and characterize the two-dimensional affine spheres that are graphs over polygons in terms of polynomials on the plane. We explain a motivation that comes from the theory of representations of fundamental groups of surfaces into a rank two Lie group.