Date/Time : 15 Oct 2020 10:00
Venue : via Zoom
Speaker : Zhilin Luo, University of Minnesota--Twin Cities

Join Zoom Meeting https://nus-sg.zoom.us/j/94022303433?pwd=b3hSZWpNTVN2VW9sU21XdThEdlJ0QT09 Meeting ID: 940 2230 3433 Password: 100202 Abstract: The local Gan-Gross-Prasad conjecture studies the restrictioin and branching problems for representations of classical and metaplectic groups . In this talk, I will talk about my proof for the tempered part of the local Gan-Gross-Prasad conejecture (multiplicity one in Vogan packets) for special orthogonal groups over any local fields of characteristic zero, which combines the work of Waldspurger (for the tempered part of the conjecture for special orthogonal groups over p-adic fields) and Beuzart-Plessis (for the tempered part of the conjecture for unitary groups over real fields) in a non-trivial way. In the proof, an indispensable result which is also of independent interest is a formula expressing the regular nilpotent germs of quasi-split reductive Lie algebras over any local fields of characteristic zero via endoscopic invariants, which was previously proved by Shelstad over $p$-adic fields. We also relate the formula with the Kostant’s sections.

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Date/Time : 08 Oct 2020 10:00
Venue : via Zoom
Speaker : Zhilin Luo, University of Minnesota--Twin Cities

Join Zoom Meeting https://nus-sg.zoom.us/j/91356784967?pwd=Q0ZxYlc5VU9UT3NCczJJNUNYTjlOZz09 Meeting ID: 913 5678 4967 Password: 256173 Abstract: I am going to talk about my joint work with D. Jiang and L. Zhang. We develop a new type of harmonic analysis on an extended symplectic groups G=G_m x Sp_2n over p-adic fields. It is associated to the Langlands gamma-functions attached to irreducible admissbile representations of G(F) and the standard representation rho of the dual group. Our work can be viewed as an extension of the work of Godement-Jacquet (which is a generalization of Tate’s thesis). We confirm a series of conjectures in the local theory of the Braverman-Kazhdan proposal in this setting.

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Date/Time : 01 Oct 2020 10:00
Venue : via Zoom
Speaker : Hang Xue, University of Arizona

Join Zoom Meeting https://nus-sg.zoom.us/j/97939482481?pwd=OW10bDJ2T2l0M2VFc0oyek1pZXNmUT09 Meeting ID: 979 3948 2481 Password: 721722 Abstract: A classical branching theorem of Weyl determines the decomposition of an irreducible representation of (compact) U(n+1) when restricted to U(n). The local Gan–Gross–Prasad conjecture puts this in the framework of local Langlands correspondence and extends it to the setting of noncompact unitary groups (and also p-adic unitary groups). We present a very simple proof of this conjecture for tempered packets of real unitary groups based on theta correspondences.  

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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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