# Analysis Seminar

#### The Program Toward Computing the Topological Degree of Toda System of Rank 2

**Speaker:**
Chang-Shou Lin, National Taiwan University

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, November 17, 2015, 2 p.m.

**Synopsis:**

It has been already shown that the generating function of the topological degree for the mean field equation is a rational function. This fact motivates us to study the nonlinear PDE from the aspects of integrable system. The theory developed from this point of view has a rich connection with hyper-elliptic curves, modular forms and Painleve VI equations. Naturally we would like to study the corresponding theory of higher rank, that is,the nonlinear elliptic PDE which are known as Toda system. Without singularity, the Toda system appears in the literature as Plucker formula in algebraic geometry. The aim of this talk is to initiate the program of calculating the topological degree for solutions of Toda systems of rank 2. The program presents many challenging analytical questions, in particular the new bobbling phenomena which could not concentrate the mass. So it leads to revisit an old theory of Brezis and Merle.