报告题目： A priori estimates and degree counting theorems for rank 2 singular Toda systems
报告人： Lei Zhang (University of Florida)
时间地点： 8月8日，14:00--14:55, 后主楼 1220
报告摘要：A Toda system is a second order elliptic system with exponential nonlinear terms defined in two dimensional spaces. It has profound connections with many fields of mathematics and physics and it has sustained extensive investigation for a few decades. In this talk I will report recent discoveries about rank 2 singular Toda systems in my joint works with Lee, Lin, Wei and Yang, using tools in quite a few seemingly little related fields.
报告题目： Translating Solitons in Euclidean Space
报告人：Ling Xiao (Rutgers University)
时间地点：8月8日，15:00--15:55 后主楼 1220
报告摘要：Mean curvature flow may be regarded as a geometric version of the heat equation. However, in contrast to the classical heat equation, mean curvature flow is described by a quasilinear evolution system of partial differential equations, and in general the solution only exists on a finite time interval. Therefore, it's very typical that the flow develops singularities.
Translating solitons arise as parabolic rescaling of type II singularities. In this talk, I shall outline a program on the classification of translating solitons. I shall also report on some recent progress we have made in the joint work with Joel Spruck.
报告题目： Boundary expansions of constant curvature graphs in the hyperbolic space
报告人：Xumin Jiang (Rutgers University)
时间地点：8月8日，16:00--16:55 后主楼 1220
报告摘要：In this talk we will introduce the machinery of boundary expansions and show how it applies to many important equations in geometry. Through constructing the boundary expansions of the solutions, we derive the optimal regularity of the solutions and understand the gap is caused by logarithmic terms.