Date/Time : 06 Apr 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Nadya Gurevich, Ben Gurion University of the Negev

The classical Schur-Weyl duality, relating representations of the symmetric group S(r) and of sl(n), admits a quantum affine generalization. We explain its relation to the Whittaker functor on the category of Iwahori-spherical genuine representations of a central cover of GL(r) of degree n. 

In particular, we deduce that the space of Whittaker functionals on such representation admits an action of an affine quantum group.

This is a joint work with Fan Gao and Edmund Karasiewicz.

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Date/Time : 04 Apr 2023 16:00
Venue : via Zoom
Speaker : Johannes Flake, MPIM Bonn

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https://nus-sg.zoom.us/j/86446315086?pwd=amtmalVXUnA0bkRnT0haRmZjeGsrQT09

Meeting ID: 864 4631 5086
Passcode: 280937

I will explain a construction of categories with a tensor product using topological operations involving manifolds, or more precisely, cobordisms. Then I will show how to analyze categories like these using algebraic and representation-theoretic ideas. The categories in question include Deligne’s interpolation categories and Khovanov-Sazdanovic’s cobordism categories. We will discuss their Grothendieck rings and, if time permits, their monoidal centers.

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Date/Time : 30 Mar 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Song Jinfeng, National University of Singapore

Let G be a reductive group over an algebraically closed field with positive characteristic, and N be the unipotent radical of a Borel subgroup. The quantum Frobenius splitting introduced by Lusztig gives an algebraic construction for a Frobenius splitting of the unipotent group N. Another important construction on N is the cluster algebra structure established by Geiss-Leclerc-Schroer. In this talk, I will explain that the algebraic Frobenius splitting on N is compatible with its cluster structure. This is based on an ongoing work.

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Date/Time : 16 Mar 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Elden Elmanto, Harvard University

Motivic cohomology is an invariant of smooth schemes which simultaneously “glues” together its etale cohomology and Chow groups. I will give a gentle introduction to the theory, its motivation, its genesis, as well as some its highlights and achievements. All this leads up to recent joint work with Matthew Morrow on its extension to singular schemes, which uses prismatic cohomology in a crucial way.

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Date/Time : 09 Mar 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : David Hansen, National University of Singapore

In recent work, Fargues-Scholze constructed a natural candidate for the local Langlands correspondence (LLC) for all reductive groups over local fields, and showed that it matches the Harris-Taylor-Henniart LLC for GL_n. It is a natural problem to ask whether their construction agrees with previously known constructions of LLC for more general groups. After giving some motivation for this problem and discussing previously known results, I will sketch a proof that for SO_2n+1 and its unique inner form, the Fargues-Scholze LLC agrees with the LLC constructed by Arthur and Moeglin.

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Date/Time : 02 Mar 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Luo Yi, National University of Singapore

In a recent work by Tasho Kaletha, local langlands conjectures were extended to a certain class of disconnected groups. Moreover, a local Langlands correspondence for disconnected tori was established, where the main ingredient is Tate-Nakayama duality in Galois hypercohomology. In this talk, we review and reformulate Kaletha’s construction. Using these local data, we show an automorphic multiplicity formula for disconnected tori over a number field.

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Date/Time : 16 Feb 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Zeev Rudnick, Tel Aviv University

Selberg computed various statistics of the number of Riemann zeros up to a given height, obtaining what was later recognized to be the same answer as for the corresponding quantity for random unitary matrices with matching eigenvalue density. We examine a corresponding problem for the eigenvalues of the Laplacian on a “random” hyperbolic surface of large genus, and describe a new perspective from the theory of moduli spaces of Riemann surfaces, as developed by Mirzakhani. I will not assume familiarity with any of the notions above.

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Date/Time : 30 Jan 2023 10:00
Venue : S17 #04-05 (SR2)
Speaker : Eric Chen, Princeton University

In the recent framework proposed by Ben-Zvi–Sakellaridis–Venkatesh, automorphic periods ought to, very roughly speaking, come in Langlands dual pairs. I will give a short introduction of this prediction and motivate the need to consider certain singular automorphic periods. In particular, I will present an example in joint work with Akshay Venkatesh, where we establish duality using a generalization of L-functions.

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Date/Time : 26 Jan 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Zhicheng Wang, University of Soochow

D. Jiang and L. Zhang proposed a conjecture which related the wavefront sets of irreducible admissible representations and the descent method in the local fields case. Recently, they and D. Liu define the arithmetic wavefront set which based on the local Gan-Gross-Prasad conjecture. In this talk, we study the relationship between wavefront sets, descent method and finite Gan-Gross-Prasad problem for finite symplectic groups. We calculate the multiplicity of an irreducible representation in the generalised Gelfand-Graev representation corresponding to finite fields analogies of the arithmetic wavefront sets. In particular, for cuspidal representations, we give certain multiplicity one theorem and show that the finite fields analogy of arithmetic wavefront sets coincides with the wavefront sets in the sense of G.Lusztig and N. Kawanaka.

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