Date/Time : 05 Oct 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Finn Wiersig, National University of Singapore

Regular holonomic D-modules form a particularly well-behaved class of systems of algebraic differential equations. Over the complex numbers, they are distinguished by two remarkable properties: the Riemann–Hilbert correspondence gives them a topological description in terms of perverse sheaves, and their derived category admits a six-functor formalism. In this talk, I will report on joint work in progress with Andreas Bode towards a p-adic analogue of this theory. Building on Diao–Lan–Liu–Zhu’s work on the p-adic Riemann–Hilbert correspondence, we introduce regular holonomic complexes of D-cap-modules on smooth rigid analytic varieties. We develop a six-functor formalism for this category, establishing stability under tensor products, internal Hom, duality, and inverse images, and discussing progress on direct images under suitable compactifiability conditions.

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Date/Time : 28 Sep 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Jack Thorne, University of Cambridge

The Langlands correspondence predicts the existence of Galois representations associated to certain automorphic representations of GL(n, AF). These are known to exist in the case that F is a CM field and the automorphic representation in question is regular algebraic (this includes, for example, the automorphic representations that should correspond to elliptic curves over imaginary quadratic fields). For arithmetic applications, it is essential to know that this automorphic to Galois dictionary satisfies compatibility with the local Langlands correspondence: in particular, when considering the restriction of the p-adic Galois representation to a p-adic decomposition group, the representation should be potentially semistable, in the sense of Fontaine, and its (semisimple) Weil—Deligne representation should be the one predicted by the local Langlands correspondence. This local-global compatibility has been proved in many cases when the p-adic Galois representation satisfies a global hypothesis (such as being `decomposed generic’). I will discuss a proof of the general case, and describe an application to the Bloch—Kato conjecture. This is joint work with A’Campo, Hevesi, and Whitmore.

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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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