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.

Add to calendar :

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.

Add to calendar :

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.

Add to calendar :

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.

Add to calendar :

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.

Add to calendar :

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.

Add to calendar :

Date/Time : 19 Jan 2023 11:00
Venue : S17 #05-12 (SR4)
Speaker : Chenyan Wu, University of Melbourne

Let $\pi$ be a cuspidal automorphic representation of a classical group or a metaplectic group. We show an exact relation between two invariants associated to $\pi$, one called the lowest occurrence index of $\pi$ which is an invariant arising from theta lifts and the other the location of the maximal positive pole of an Eisenstein series attached to $\pi$ and a character. As an application, We show that certain global Arthur packets cannot contain cuspidal automorphic representations.

Add to calendar :

Date/Time : 12 Jan 2023 10:00
Venue : S17 #04-05 (SR2)
Speaker : Stefan Dawydiak, Max Planck Institute for Mathematics in Bonn (MPIM)

In the 1980s, Kazhdan-Lusztig and independently Ginzburg showed that the affine Hecke algebra $H$ can be realized as the Grothendieck group of the category of coherent sheaves on the Steinberg variety. The correct coherent Hecke category was however found only later, by Bezrukavnikov. A crucial ingredient in this coherent categorification of $H$ is viewing the Steinberg variety as a derived scheme.

On the other hand, Lusztig’s asymptotic Hecke algebra $J$ is a certain based ring receiving a map from $H$, via which its representation theory is closely related to that of $H$. In the 1990s, Xi showed that the best-understood direct summand $J_0$ of $J$ can be realized as the Grothendieck group of coherent sheaves on the square of the flag variety, and Ginzburg gave a K-theoretic definition of the map from $H$ to $J_0$. In this talk we will explain how to upgrade this realization to a monoidal category receiving a natural monoidal functor from the coherent Hecke category. A crucial ingredient is again to consider a derived enhancement, this time of the flag variety.

Add to calendar :

Date/Time : 11 Nov 2022 14:00
Venue : via Zoom
Speaker : Liping Li, Hunan Normal University

Join Zoom Meeting
https://nus-sg.zoom.us/j/85349169300?pwd=bE9Ed2ZLelNHdVpjSFV5YnEwdlJpUT09

Meeting ID: 853 4916 9300
Passcode: 176749

Abstract: In this talk we describe an approach to classify irreducible discrete representations of infinite linear groups, based on Artin’s theorem connecting discrete representations of topological groups and sheaves of modules over atomic sites as well as some recent development in representation stability theory.

Add to calendar :