Date/Time : 29 Apr 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Heejong Lee, Korea Institute for Advanced Study (KIAS)

Given a Galois representation attached to a regular algebraic cuspidal automorphic representation, the Hodge–Tate weight of the Galois representation is matched with the weight of the automorphic representation. Serre weight conjectures are mod p analogue of such a correspondence, relating ramification at p of a mod p Galois representation and Serre weights of mod p algebraic automorphic forms. In this talk, I will discuss how to understand Serre weight conjectures and modularity lifting as a relationship between representation theory of finite groups of Lie type (e.g. GSp4(Fp)) and the geometry of p-adic local Galois representations. Then I will explain the proof idea in the case of GSp4. This is based on a joint work with Daniel Le and Bao V. Le Hung.

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Date/Time : 15 Apr 2026 16:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Tomoyuki Abe, Kavli IPMU, Tokyo

Deligne showed that the diagonal series of an algebraic power series of n variables over a field of positive characteristic remains algebraic. He deduced this theorem using geometric method in the case n=2, and showed the general case using purely algebraic method. However, he expected a more direct proof of that fact, and gives a conjectural bound of the degree of algebraicity. The conjectural bound had been verified by Adamczewski and Bell using elementary method. We revisit this question using arithmetic D-module. This is a joint work with R. Crew.

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Date/Time : 08 Apr 2026 16:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Xiangqian Yang, Peking University

Clozel, Harris and Taylor proposed a generalized Ihara’s lemma for definite unitary groups. In this talk, we prove some cases of their conjecture under the assumption of banal coefficients. The proof relies on the unipotent categorical local Langlands correspondence established by Zhu. We also discuss certain properties of the coherent sheaf associated to the space of automorphic forms under the categorical local Langlands functor.

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Date/Time : 30 Mar 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ian Gleason, National University of Singapore

This is a sequel to the previous talk. In this talk I will describe the challenges tackled in order to construct the comparing functor. Depending on time constraints, I might also discuss the strategy to show that the constructed functor is an equivalence.

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Date/Time : 16 Mar 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Ian Gleason, National University of Singapore

We show a folklore conjecture stating that two categorical enhancements of the automorphic side of the local Langlands correspondence agree. The first enhancement appears in Fargues–Scholze’s formulation of the categorical local Langlands correspondence, and the second one appears in Zhu’s formulation. This is joint work with Hamann, Ivanov, Lourenco, Zou.

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Date/Time : 02 Mar 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Chenji Fu, University of Bonn

Eteve computed the Genestier-Lafforgue L-parameters for depth-zero representation for a equal-characteristic local field. I will explain how to adapt his method to the setting of Fargues-Scholze. We use certain ”smoothness” and ”properness” of the stack of shtuka to reduce the question to the local Hecke stack, where we can do an explicit computation using hyperbolic localizations following the work of ALWY on central sheaves in mixed characteristic.

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Date/Time : 02 Feb 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Yihang Zhu, Tsinghua University

The Langlands-Kottwitz method seeks to express Frobenius-Hecke traces on the cohomology of Shimura varieties in terms of objects in local harmonic analysis which enter the Arthur-Selberg trace formula, namely orbital and twisted orbital integrals. As a local analogue, we present a formula relating the cohomology of local Shimura varieties with twisted orbital integrals. This formula bridges the point-counting formula for Shimura varieties with the point-counting formula for Igusa varieties, a manifestation of the Mantovan product relation. As an application of our local formula, we explain a new categorical-Langlands-based approach towards Rapoport’s conjecture on the vanishing of certain twisted orbital integrals, which is itself a key ingredient in the global Langlands-Kottwitz method for a non-quasi-split prime. This is joint work with Rong Zhou.

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Date/Time : 15 Dec 2025 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Yuta Takaya, Tokyo University

In the local Langlands program, both local Shimura varieties and type theory play important roles. Although the relationship between these two approaches remains largely open, starting from the work of Yoshida and Boyarchenko-Weinstein, it has been observed that certain affinoids around CM points in Lubin-Tate spaces reflect the associated type theory. In this talk, I will introduce analogous affinoids around unramified CM points in general local Shimura varieties, and explain the relation to regular depth-zero supercuspidal representations. If time permits, I will provide an outlook on the extension to positive depth.

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Date/Time : 08 Dec 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yuta Takaya, Tokyo University

The relation between period integrals and L-functions, studied since the work of Hecke and Tate, has recently been reformulated by Ben-Zvi–Sakellaridis–Venkatesh as relative Langlands duality. In this talk, I will present a version of this duality, the normalized period conjecture, in the framework of the categorical local Langlands correspondence à la Fargues-Scholze. I will describe computations for the Iwasawa-Tate and Hecke periods that support this conjecture, and discuss how it leads to a relation between distinguished representations and distinguished L-parameters. This talk is based on joint work with Milton Lin.

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