Abstract: Toda system is a system of two dimensional elliptic equations with exponential non-
linearity. It is well known that the study of Toda systems is important not only to Chern-Simons
models in Physics, but also to the understanding of various topics in Algebraic Geometry. One
major goal in the study of Toda system on Riemann surfaces is to completely understand the
asymptotic behavior of fully bubbling solutions. In this talk I will report a recent joint work with
Juncheng Wei and Chang-shou Lin that describes the fully bubbling solutions in the sharp form.