9:30-10:30

Zhixiang Wu (USTC)

Title: On the derived category of some locally analytic representations of GL2(Qp)

Abstract: The cohomology groups of equivariant vector bundles on the Drinfeld upper half plane give rise to supercuspidal locally analytic representations of GL2(Qp). These representations are closely related to two-dimensional p-adic de Rham Galois representations, by the Breuil–Strauch conjecture, proved by Dospinescu and Le Bras. In this talk, I will discuss some ongoing work with Zhenghui Li and Benchao Su towards a geometrization of the derived category of these representations, in the spirit of the categorical p-adic local Langlands correspondence.

11:0-12:00

Tian Qiu （PKU）

Title: The Fontaine operator at cusps of modular curves at infinite level

Abstract: We explicitly calculate Pan's geometric intertwining operator and the Fontaine operator on modular curves at infinite level via q-expansions, using Heuer's theory of cusps at infinite level. We prove that these two operators coincide on such expansions up to an explicit constant. As an application, we combine this result with q-expansion principles to provide a new proof of Pan's theorem that these operators are equal on the locally analytic vectors of completed cohomology of modular curves.

1:30-2:30

Zicheng Qian (AMSS)

Title: On some restriction to T maps

Abstract: Motivated by the matching between Breuil-Schraen L invariants and Fontaine-Mazur L invariants via the Drinfeld space, we study certain restriction to T maps for smooth/locally analytic cohomology of smooth/locally analytic generalized Steinberg. This is an ongoing joint work with Benchao Su and Arnaud Vanhaecke.

3:00-4:00

Reinier Sorgdrager (Universite Paris-Saclay)

Title: Upper GK-bound for p-adic Banach representations with infinitesimal character

Abstract: Let p>2 and K be a finite extension of Q_p. In recent work I have shown that an admissible p-adic Banach representation of GL2K has Gelfand-Kirillov dimension at most the degree [K:Q_p] as soon as its locally analytic vectors have an infinitesimal character. In work yet to appear I adapt its method to ``p-adic Banach representations in families with infinitesimal characters in families'' -- still for GL2K.

I will motivate the result by some consequences to the p-adic Langlands program, such as a generalization of the GK-bound of Breuil-Herzig-Hu-Morra-Schraen beyond K unramified. Then I will give a quick overview of the above notions and explain why this result might be surprising.