Description: This talk will use the Ricci Flow to put curvature bounds on manifolds in three cases: Euler characteristic of a given surface is positive, zero, or negative. Using these bounds one can show that in each case the metric tends toward a limit metric on the surface that has constant curvature. This talk will focus on the latter two cases and if time permits the more difficult case of positive Euler characteristic will be discussed.
Partial proof of the Uniformization Theorem using Ricci Flow
Mar. 04, 2014 1pm (MATH 220)
Grad Algebra/Logic
Agnes Szendrei Burnside's Theorem on Transitive Permutation Groups of Prime Degree, Part 2
Mar. 04, 2014 2pm (MATH 350)
Lie Theory
C. Ryan Vinroot
X
There are several very good reasons to understand the real-valued characters of finite groups of Lie type, including applications in the general theory of real characters of finite groups, and applications in the representations of p-adic group. In the case that is a connected reductive group with connected center, defined over a finite field by Frobenius morphism F, we are able to parameterize the real-valued characters of the finite group using the Lusztig parameters, or Jordan decomposition, of the characters. The main tool to prove this parameterization is by using a result of Digne and Michel, who describe the Jordan decomposition map as the unique such map with a certain list of properties, where this uniqueness can be exploited. The parameterization we obtain leads one to conjecture how to predict the Frobenius-Schur indicator of a real-valued character of . This work is joint work with Bhama Srinivasan from the University of Illinois at Chicago.
Partial proof of the Uniformization Theorem using Ricci Flow