On elliptic Toda systems

Toda systems are important examples of integrable systems, and we consider the version using the Laplacian on the plane. They are generalizations of the Liouville equation to simple Lie algebras. As such, they are related to 2-dimensional conformal geometry and harmonic maps. 

In this talk, we will discuss the classification of solutions to such Toda systems and the quantization result on their total masses. Such total masses have applications to the local blowup analysis of the  mean field equations.