Speakers: Gabriel Dospinescu (Ecole normale superieure de Lyon, CNRS),

                 Alexandre Pyvovarov (Morningside Center, Chincese Academy of Sciences),

                 Haoran Wang (Yau Mathematical Sciences Center, Tsinghua University),

                 Shanwen Wang (Shanghai Center for Mathematical Sciences, Fudan University),

                 Bin Zhao (Morningside Center, Chincese Academy of Sciences)

Schedule: 09:30-10:30  Gabriel Dospinescu

                 11:00-12:00  Bin Zhao

                 12:00-13:30  Lunch break

                 13:30-14:30  Haoran Wang

                 14:50-15:50  Alexandre Pyvovarov

                 16:10-17:10  Shanwen Wang

Title & Abstract:

Gabriel Dospinescu,

Title:  p-adic étale Cohomology of Some p-adic Period Domains

Abstract: We will explain work in progress with Colmez, Hauseux and Niziol whose aim is to adapt Orlik's computation of the l-adic cohomology of p-adic period domains attached to basic classes and quasi-split groups to the case l=p.

Alexandre Pyvovarov,

Title: Some New Cases of the Breuil-Schneider Conjecture

Abstract: Let F and E be two finite extensions of Qp such that E is large enough. Let r : Gal(F_bar/F) -> GL_n(E) be a Galois representation. In 2013 Caraiani, Emerton, Gee, Geraghty, Paskunas and Shin have constructed an E -Banach representation V(r) of GL_n(F). The authors have hypothesized that the representation V(r) corresponds to Galois representation r under hypothetical p-adic Langlands correspondence. In this work, we show that, under certain assumptions on r, the locally algebraic vectors of V(r) are isomorphic to an irreducible locally algebraic representation. This locally algebraic representation can be determined explicitly via the classical local Langlands correspondence and the knowledge of the Hodge-Tate weights of the Galois representation. From this we can derive new cases of the Breuil-Schneider conjecture.

Haoran Wang,

Title: On the Mod p Cohomology of Shimura Curves

Abstract: The mod p local Langlands correspondence is well-understood for GL2(Qp), but it is still very mysterious in other cases. In this talk, I will discuss some results on the mod p correspondence for GL2(F) when F is a finite unramified extension of Qp. This is a joint work in progress with Yongquan Hu.

Shanwen Wang,

Title: Modular Symbol and Kato's Euler System

Abstract: In this talk，we will explain the relation between modular symbol and Kato'Euler system in an explicit way which can be used as an possible input toward a proof of Iwasawa Main conjecture for modular forms. This talk is based on a joint work with Pierre Colmez.

Bin Zhao,

Title: Spectral Halo for Hilbert Eigenvarieties

Abstract: It is conjectured by Coleman-Mazur and Buzzard-Kilford that over the boundary annuli of weight space, the eigencurve is a disjoint union of infinitely many connected components. In the previous work by Ruochuan Liu, Daqing Wan and Liang Xiao, they gave an almost complete answer to this conjecture by studying the eigencurve associated to a definite quaternion algebra over Q. In this talk, I will explain a recent joint work in progress with Rufei Ren on the generalization of their results to certain Hilbert eigenvarieties.