Time:

9-10 Lue Pan

10:30-11:30 Ziquan Zhuang

14:30-15:30 Lue Pan

16:00-17:00 Ziquan Zhuang

Lue Pan

Title: Automorphy lifting theorems
Abstract: Automorphy/Modularity lifting theorems were first introduced in Wiles's proof of Fermat's last theorem and provide a very powerful technique for proving that certain Galois representations are automorphic. We will discuss some recent development of automorphy lifting theorems and its applications in the Langlands program.

Ziquan Zhuang

Title: Stability of Singularities

Abstract: Donaldson and Sun conjectured that the metric tangent cones of smoothable Kähler-Einstein Fano varieties only depend on their algebraic structure. Later Li and Xu proposed the Stable Degeneration Conjecture as a generalization; it predicts that every mild singularity has a canonical degeneration that shares many features of the metric tangent cones. I'll survey some recent progress in local K-stability that solves these conjectures, and discuss some related open problems.