Date/Time : 14 Sep 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Jack Sempliner, University of California (Los Angeles)

We will discuss a new result on the p-adic geometry of Igusa stacks, which allows one to relate the p-adic geometry of Shimura varieties for a pair of groups $G, G’$ which are global extended pure inner forms. Using this geometric input and the spectral action of Fargues-Scholze, we will discuss how this input may be used to prove the existence of Hecke-equivariant cohomological “Jacquet-Langlands” maps between the cohomology (even with integral or torsion coefficients) of the two Shimura varieties of abelian type associated to $G, G’$.

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Date/Time : 07 Sep 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : David Hansen, National University of Singapore

I will formulate a collection of vanishing conjectures in the Fargues-Scholze setting, which describe the maps on suitable Grothendieck groups induced by Eisenstein functors, constant term functors, and the gluing functors between strata of Bun_G. I will also discuss the relationships among these conjectures, and explain how they imply a very general form of the Bertoloni Meli-Harris-Viehmann conjecture (which I will also recall in detail). I will then sketch a proof of the vanishing conjectures (and hence a proof of the generalized BMHV conjecture). Joint work in progress with Linus Hamann and Peter Scholze.

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Date/Time : 31 Aug 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : David Hansen, National University of Singapore

I will formulate a collection of vanishing conjectures in the Fargues-Scholze setting, which describe the maps on suitable Grothendieck groups induced by Eisenstein functors, constant term functors, and the gluing functors between strata of Bun_G. I will also discuss the relationships among these conjectures, and explain how they imply a very general form of the Bertoloni Meli-Harris-Viehmann conjecture (which I will also recall in detail). I will then sketch a proof of the vanishing conjectures (and hence a proof of the generalized BMHV conjecture). Joint work in progress with Linus Hamann and Peter Scholze.

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Date/Time : 24 Aug 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Alberto Vezzani, University of Milan

We present how the framework of rigid analytic motivic homotopy theory provides streamlined definitions of relative Hyodo-Kato cohomologies, constructibility results and comparison isomorphisms to de Rham cohomology, while also proving generalizations of ell-adic local monodromy theorems. This is work in progress with Fabrizio Andreatta and Federico Binda.

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Date/Time : 17 Aug 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Katsuyuki Bando, Keio University

The geometric Satake equivalence is the categorification of the Satake isomorphism. Its derived version, “the derived geometric Satake equivalence,” is proved by Bezrukavnikov-Finkelberg in the case of equal characteristic. In this talk, we will explain a new affine Grassmannian which connects an equal characteristic affine Grassmannian and Zhu’s Witt-vector affine Grassmannian. As a result, we deduce the derived Satake equivalence in mixed characteristic. By the same argument, we also obtain the mixed characteristic version of Bezrukavnikov’s equivalence between two categorifications of an affine Hecke algebra. Moreover, we explain the derived geometric Satake equivalence on the Beilinson–Drinfeld Grassmannian with one leg in mixed characteristic.

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Date/Time : 04 May 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Thomas Bitoun, Shanghai Institute for Mathematics and Interdisciplinary Sciences

Let Z be the germ of a complex hypersurface isolated singularity of equation f. We consider the family of analytic D-modules generated by the powers of 1/f and relate it to the pole order filtration on the de Rham cohomology of the complement of {f=0}. This work revisits Vilonen’s characterization of the intersection homology D-module.

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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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