Number Theory Seminar

Seminar information archive ~06/17Next seminarFuture seminars 06/18~

Date, time & place Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Naoki Imai, Shane Kelly

2019/10/16

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Liang Xiao (BICMR, Peking University)
On slopes of modular forms (ENGLISH)
[ Abstract ]
In this talk, I will survey some recent progress towards understanding the slopes of modular forms, with or without level structures. This has direct application to the conjecture of Breuil-Buzzard-Emerton on the slopes of Kisin's crystabelline deformation spaces. In particular, we obtain certain refined version of the spectral halo conjecture, where we may identify explicitly the slopes at the boundary when given a reducible non-split generic residual local Galois representation. This is a joint work in progress with Ruochuan Liu, Nha Truong, and Bin Zhao.