Date/Time : 23 Sep 2020 15:00
Venue : via Zoom
Speaker : Hirotaka Kakuhama, Kyoto University

Join Zoom Meeting https://nus-sg.zoom.us/j/93822139520?pwd=SGhwZUMrWUFRRjdCcm9zQkk0U05sZz09 Meeting ID: 938 2213 9520 Password: 884511 Abstract: Let (H,G) be a reductive dual pair consisting of quaternion unitary groups over a local field. I will talk about the behavior of formal degrees under the theta correspondence for (H,G), which extends a work of Gan-Ichino for orthogonal-symplectic dual pairs and unitary dual pairs. The main ingredient is a precise analyzation of the local Siegel-Weil formula: which is a different point from Gan-Ichino’s work. Moreover, I will mention about an application to the formal degree conjecture.

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Date/Time : 17 Sep 2020 09:00
Venue : via Zoom
Speaker : Chen Wan , Rutgers University, Newark

Join Zoom Meeting https://nus-sg.zoom.us/j/94523183102?pwd=QXB4bmNhNTFGMFBaWStGRGg1S2wvZz09 Meeting ID: 945 2318 3102 Password: 908567 Abstract: In this talk, I will discuss the local multiplicity for the unitary Shalika model. By proving a local trace formula for the unitary Shalika model and a twisted local trace formula for the Shalika model, we are able to explicitly compute the multiplicity of the unitary Shalika model for all the discrete series. This is a joint work with R. Beuzart-Plessis.

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Date/Time : 09 Sep 2020 15:00
Venue : via Zoom
Speaker : Raphaël Beuzart-Plessis, Université d’Aix-Marseille

Join Zoom Meeting https://nus-sg.zoom.us/j/94485648813?pwd=d2pRWVJoVWdybTNhems3L2V4VkQvZz09 Meeting ID: 944 8564 8813 Password: 690359 Abstract: This talk concerns a global conjecture of Gan-Gross-Prasad relating the non-vanishing of certain automorphic periods on unitary groups to the non-vanishing of certain Rankin-Selberg L-functions at their center of symmetry. It also admits a refinement, proposed by Ichino-Ikeda, in the form of an exact identity connecting these two invariants. Following an approach initiated by Jacquet-Rallis of comparing two (relative) trace formulas, W. Zhang and more recently Y. Liu, W.Zhang, X. Zhu and myself have established both of these conjectures for cuspidal representations that are “stable” i.e. whose quadratic base-change is again cuspidal. In this talk, I will explain how to deal with the remaining cuspidal representations, sometimes called “endoscopic”, to which the conjectures apply through a fine spectral expansion of parts of the Jacquet-Rallis trace formula for general linear groups. This is joint work with Pierre-Henri Chaudouard and Michal Zydor..

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Date/Time : 02 Sep 2020 15:00
Venue : via Zoom
Speaker : Sug Woo Shin, University of California, Berkeley

Zoom link: https://nus-sg.zoom.us/j/99468790870?pwd=SHIveFFOalkvdTczNTVteWdJbmMzdz09 Meeting ID: 994 6879 0870 Password: 374233 I will present my joint work with Arno Kret, where we construct a GSpin(2n)-valued ell-adic Galois representation attached to a cuspidal cohomological automorphic representation pi of a suitable quasi-split form of GSO(2n) over a totally real field, under the hypothesis that pi has a Steinberg component at a finite place. This uses input from the cohomology of certain Shimura varieties for GSO(2n); as such we need to take a suitable form of GSO(2n) depending on the parity of n. (We take the split form if and only if n is even.) The relevant preprint is available at https://math.berkeley.edu/~swshin/GSO.pdf.      

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Date/Time : 26 Aug 2020 15:00
Venue : via Zoom
Speaker : Lu Ming, Sichuan University

Join Zoom Meeting https://nus-sg.zoom.us/j/99335000776?pwd=UFVJNnN1ZTJMK1MzQlpFWnVSckwrQT09 Meeting ID: 993 3500 0776 Password: 359589 Abstract: A quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an i-quantum group). A quantum group can be viewed as an example of i-quantum groups associated to symmetric pairs of diagonal type. In this talk, we present a new Hall algebra construction of i-quantum groups. Our approach leads to monomial bases, PBW bases, and braid group actions for i-quantum groups. In case of symmetric pairs of diagonal type, our work reduces to a reformulation of Bridgeland’s Hall algebra realization of a quantum group, which in turn was a generalization of earlier constructions of Ringel and Lusztig for half a quantum group. This is joint work with Weiqiang Wang.

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Date/Time : 25 Feb 2020 10:00
Venue : S17 #04-04 SR3
Speaker : Hirotaka Kakuhama, Kyoto University

Date/Time:25 Feb 2020 10:00 Venue: S17 #04-04 SR3 Speaker: Hirotaka Kakuhama, Kyoto University The Doubling $\gamma$-factor over Local Function Fields. The analytic definition of the standard local $\gamma$-factor of irreducible representations of classical groups over $\mathbb{R}$, $\mathbb{C}$, and $p$-adic fields has been established by using the doubling method by Lapid-Rallis, Gan, and the speaker. In this talk, I will discuss about the case of local function fields. First, I will explain the definition of the $\gamma$-factor. Then, I will prove that the $\gamma$-factor satisfies some properties which characterize it. Add to calendar: 

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Date/Time : 12 Feb 2020 10:00
Venue : S16 #03-04
Speaker : Ma Jiajun, Shanghai Jiao Tong University

Date/Time:12 Feb 2020 10:00 Venue: S16 #03-04 Speaker: Ma Jiajun, Shanghai Jiao Tong University Cells and Primitive Ideals The theory of left/right/two side cells of Coxeter groups has become a ubiquitous tool in the representation theory of reductive groups. In this talk, I will give a survey of some basic facts of cells. Then I will focus on the classical Weyl groups and introduce the related combinatorial objects attaching to cells/Weyl group elements. In the end, I will explain the relationship between left cells and primitive ideals in the universal enveloping algebra. Add to calendar: 

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Date/Time : 05 Feb 2020 10:00
Venue : S17 #04-04 SR3
Speaker : Bao Huanchen, NUS

Date/Time:05 Feb 2020 10:00 Venue: S17 #04-04 SR3 Speaker: Bao Huanchen, NUS Asymptotic Hecke algebras, part 2 We explain Lusztig’s construction of the asymptotic Hecke algebras. Add to calendar: 

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Date/Time : 29 Jan 2020 10:00
Venue : S17 #04-04 SR3
Speaker : Bao Huanchen, NUS

Date/Time:29 Jan 2020 10:00 Venue: S17 #04-04 SR3 Speaker: Bao Huanchen, NUS Asymptotic Hecke algebras, part 1 We explain Lusztig’s construction of the asymptotic Hecke algebras. Add to calendar: 

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