by Liang Xiao (BICMR, Peking University)

Centre de conférences Marilyn et James Simons (IHES)

Centre de conférences Marilyn et James Simons


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

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.

Organized by

Ahmed Abbes