Speaker: Liang Xiao(肖梁) (University of Connecticut)

Time and venue:
(82J12 on W., 82J04 on T and Th., and please note the different time on each day)
July 7. Tues. 16:00-17:00 82J04
July 8 Wedn. 14:00-16:00 82J12
July 9 Thur. 16:00-17:00 82J04

July 14 Tues. 14:00-16:00 82J04
July 15 Wedn. 14:00-16:00 82J12
July 16 Thur. 14:00-16:00 82J04

Abstract: I will explain the Taylor-Wiles-Kisin patching argument in the proof of various modularity lifting theorems. We focus on the modern viewpoint of functorial patching argument, in the spirit of geometric Breuil-Mezard conjecture. We shall also discuss some recent result by Emerton-Gee-Savitt on understanding the lattice in the cohomology of Shimura curves, and the six-authors paper on patching of completed cohomology. If time permits, I will discuss some further topics on this subject.