Date/Time : 10 Nov 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Jhan-Cyuan Syu, National University of Singapore

Let G be a split connected reductive group over a non-archimedean local field. The categorical local Langlands conjecture (CLLC) predicts an equivalence between lisse-étale sheaves on Bun_G, the moduli stack of G-bundles on relative Fargues-Fontaine curves, and ind-coherent sheaves on Par_G, the moduli stack of l-adically continuous L-parameters. One question is to find t-structures on the automorphic side and the spectral side such that the categorical equivalence is t-exact. On the automorphic side, there is a perverse t-structure. However, the story is still mysterious on the spectral side. After localizing at certain types of L-parameters, we can say more about t-structures. In this talk, we will localize at the trivial L-parameter and compute the multiplicity of certain perverse sheaves with the help of CLLC.

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Date/Time : 03 Nov 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Joao Lourenco, Universite Sorbonne Paris Nord

Given a reductive group $G$ over a $p$-adic field $F$ with parahoric group model $\mathcal{G}$ over the ring of integers $O$, we can consider its associated flag variety using Witt vectors on perfect $k$-algebras: this is representable by a perfect ind-scheme by a deep theorem of Bhatt-Scholze. This time, we want to study its $\mathbb{F}_p$-étale cohomology, but its behavior is linked with coherent cohomology due to the Artin-Schreier sequence. We are going to explain how the Cohen-Macaulayness of a perfect scheme relates to its perverse $\mathbb{F}_p$-sheaves. Then, we will explain a new and uniform proof of this property for Schubert varieties in the minuscule range based on inversion of adjunction. This is joint work with Robert Cass.

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Date/Time : 27 Oct 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Joao Lourenco, Universite Sorbonne Paris Nord

The geometric Satake equivalence of Mirkovic-Vilonen identifies the monoidal category of perverse sheaves with l-adic coefficients on the Hecke stack of a split reductive group G over a Laurent series field with the monoidal category of representations of the Langlands dual of G. However, from the point of view of the Langlands program, it is also natural to consider ramified groups and their special parahoric models. With rational l-adic coefficients, ramified Satake was proved by Zhu and Richarz, exploiting semisimplicity of the category of representations. We extend these equivalences to integral and modular l-adic coefficients, via a careful study of semi-infinite orbit filtrations that allow us to bypass the lack of fusion, and a delicate analysis of fixed point group schemes. This is joint work with Achar, Richarz and Riche.

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Date/Time : 13 Oct 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : :Si Ying Lee, National University of Singapore

I will talk about constructing integral models for Hecke correspondences in both the global and local settings, using the theory of F-gauges. Using these integral models, I will explain how one can construct integral Hecke actions on coherent cohomology for compact abelian type Shimura varieties, proving a conjecture of Fakhruddin-Pilloni. This is joint work in progress with Keerthi Madapusi.

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Date/Time : 29 Sep 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Yifei Zhao, University of Muenster

Around 10 years ago, Weissman constructed the local Langlands correspondence (LLC) for covers of split tori defined by Brylinski-Deligne extensions. An intriguing phenomenon is that the LLC map is not surjective in general. The goal of my talk is to relate this phenomenon to the existence of “extended pure inner forms” of covers. This is based on joint work with Luozi Shi.

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Date/Time : 08 Sep 2025 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dai Wenhan, National University of Singapore

Under categorical local Langlands, certain natural coherent sheaves on Vogan stacks give rise to matching automorphic sheaves on Bun_G, which are generally hard to understand. Understanding the stalks of these automorphic sheaves at points of Bun_G would crucially provide a mechanism for the explicit matching of objects along the categorical local Langlands functor. Despite its importance, the general behavior of these stalks remains largely mysterious. In this talk we will study these sheaves for G=GLn at the Vogan stack of the Steinberg parameter. Some recent conjectures predict that at basic points, these stalks are given by generalized Steinberg representations of inner forms of G, up to degree shifts. After formulating the main conjecture, I will report some progress towards its proof in a special case on the degree-zero component of Bun_G, achieved through combinatorial computations inspired by Hansen. If time permits, I will also present an application of the result to cohomology of local Shimura varieties.

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Date/Time : 25 Aug 2025 14:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Adeel Khan, Academia Sinica

I will discuss a new type of pullback operation on perverse sheaves, which is defined for morphisms of complex algebraic stacks equipped with a certain extra structure, namely that of a so-called relative exact (-1)-shifted symplectic fibration. These perverse pullbacks are closely related to classical operations such as vanishing cycles functors and the Fourier-Sato transform. They also vastly generalize the theory of Donaldson-Thomas invariants of Calabi-Yau threefolds, and we will sketch how they lead to a proof of a conjecture of Joyce about their functoriality. Time permitting, I will attempt to briefly survey some applications of these constructions to topics like cohomological Hall algebras, curve counting on Landau-Ginzburg models, and the period sheaves for Hamiltonian G-spaces conjectured by Ben-Zvi, Sakellaridis, and Venkatesh. This is a report on joint work in progress with Tasuki Kinjo, Hyeonjun Park, and Pavel Safronov.

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