Date/Time : 21 Nov 2019 10:00
Venue : S17 #04-06 SR1
Speaker : Yao Cheng, Institute of Mathematics, Academia Sinica

Date/Time:21 Nov 2019 10:00 Venue: S17 #04-06 SR1 Speaker: Yao Cheng, Institute of Mathematics, Academia Sinica On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions This is the last talk of a series of four talks on the discussion of the papers [Sak08], [Sak13] and [Sak12]. The present talk consists of two parts. In the first part of this talk I will first briefly review some results in the previous talks and then discuss [Sak13, Part 3] on applications of the explicit formulae for spherical functions on spherical varieties. In the second part of this talk I will give an overview of the paper [Sak12] with emphasis on section 3 and section 4 which I hope it can be served as an introduction to that paper. References [Sak08] Yiannis Sakellaridis. On the unramified spectrum of spherical varieties over p-adic fields. Compositio Mathematica, 144(4):978–1016, 2008. [Sak12] Yiannis Sakellaridis. Spherical varieties and integral representations of L-functions . Algebra number theory, 6(4):611–667, 2012. [Sak13] Yiannis Sakellaridis. Spherical functions on spherical varieties. American Journal of Mathematics, 135(5):1291–1381, 2013. Add to calendar: 

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Date/Time : 21 Nov 2019 10:00
Venue : S17 #04-06 SR1
Speaker : Yao Cheng, Institute of Mathematics, Academia Sinica

This is the last talk of a series of four talks on the discussion of the papers [Sak08], [Sak13] and [Sak12]. The present talk consists of two parts. In the first part of this talk I will first briefly review some results in the previous talks and then discuss [Sak13, Part 3] on applications of the explicit formulae for spherical functions on spherical varieties. In the second part of this talk I will give an overview of the paper [Sak12] with emphasis on section 3 and section 4 which I hope it can be served as an introduction to that paper. References [Sak08] Yiannis Sakellaridis. On the unramified spectrum of spherical varieties over p-adic fields. Compositio Mathematica, 144(4):978–1016, 2008. [Sak12] Yiannis Sakellaridis. Spherical varieties and integral representations of L-functions . Algebra number theory, 6(4):611–667, 2012. [Sak13] Yiannis Sakellaridis. Spherical functions on spherical varieties. American Journal of Mathematics, 135(5):1291–1381, 2013.  

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Date/Time : 13 Nov 2019 10:00
Venue : S16 #03-09
Speaker : Wan Xiaolei,

Date/Time:13 Nov 2019 10:00 Venue: S16 #03-09 Speaker: Wan Xiaolei The formula with L-value of the spherical varieties This is the third talk of Sakellaridis’ work on Spherical Varieties and Spherical Functions. We will give a brief review of the first two talks, then we complete one of the main theorems of this talk. Namely, under some conditions, we can give an explicit formula of the eigenfunctions of the Hecke algebra in the space of spherical functions on a spherical variety. And then we can define the L-function of spherical varieties which related to the special value of the eigenfunctions. Finally we show some examples of the calculation of the L-value. The importance of the L-value lies in its relationship with the period integrals of automorphic forms. Add to calendar: 

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Date/Time : 06 Nov 2019 10:00
Venue : S16 #03-09
Speaker : Tian Fangyang, National University of Singapore

Date/Time:06 Nov 2019 10:00 Venue: S16 #03-09 Speaker: Tian Fangyang, National University of Singapore Spherical Functions on Spherical Varieties – Explicit Formula of Eigenfunctions of Hecke Algebra This talk is a sequel of the report of Sakellaridis’ work on Spherical Varieties and Spherical Functions. Based on the geometric background which Zou Jialiang talked about last week, we will in this talk focus on the representation theoretic aspect of spherical varieties. We will start from some Bruhat-Mackey theorem on spherical varieties (distributions on orbit-spaces) and its relation with the standard interwining operators. Under a suitable normalization of these intertwining operators via the Fourier transform (of Braverman-Kazhdan), we will present Sakellaridis Theorem 1.2.1 in his 2013 paper, which provides an explicit formula for the eigenfunction of the Hecke algebra in the space of spherical functions on a spherical variety. Add to calendar: 

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Date/Time : 30 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Zou Jialiang,

Date/Time:30 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Zou Jialiang Structure of Spherical Varieties Given a spherical variety X for a group G over a non-Archimedean local field k, Sakellaridis and Venkatesh have formulated an approach to study the spectral decomposition of L^2(X) in the framework of Langlands functoriality. We will study this theory in the next few weeks. In this talk, I will present some basic knowledge of spherical variety including 1. The definition of spherical variety 2. The Luna-Vust theory about the classification of embeddings of a spherical pair H/G. Some special embeddings like toroidal embedding and wonderful compactification. 3. The knop action on spherical and the little Weyl group. 4. The dual group G_X^{\vee} of the spherical variety and the distinguished morphism. 5. Some rationality properties of the spherical variety. Reference: 1. Sakellaridis, Y. (2008). On the unramified spectrum of spherical varieties over p-adic fields. Compositio Mathematica, 144(4), 978-1016. Part 2&3. 2. Sakellaridis, Y., Venkatesh, A., & Venkatesh, A. (2017). Periods and harmonic analysis on spherical varieties. Société mathématique de France. Chapter 2. Add to calendar: 

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Date/Time : 23 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Allan Merino, National University of Singapore

Date/Time:23 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Allan Merino, National University of Singapore Character Varieties Giving a pair (Gamma, G), where Gamma is a finitely generated group and G a complex algebraic reductive group, we define the GIT-quotient Hom(Gamma, G) // G: it’s the character variety corresponding to (Gamma, G). One can determine a set of generators when G = SL(V), Sp(V) and O(V) using results of Weyl and Procesi, and for G = SO(V) using a paper of Zhu-Aslaksen-Tan and a recent result of Sikora. In my talk, I will explain first how can we determine these generators. At the end, I will present an ongoing project, joint with Clement Guerin, concerning the character variety of Spin(n) and G2. Add to calendar: 

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Date/Time : 16 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Wang Chuijia,

Date/Time:16 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Wang Chuijia Geometric constructions of local Langlands correspondence for p-adic groups (II) In this talk, we review several different approaches to geometric constructions of local Langlands correspondence which are in different flavour. Add to calendar: 

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Date/Time : 09 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Wang Chuijia,

Date/Time:09 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Wang Chuijia Geometric constructions of local Langlands correspondence for p-adic groups In this talk, we review several different approaches to geometric constructions of local Langlands correspondence which are in different flavor. Add to calendar: 

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Date/Time : 02 Oct 2019 10:00
Venue : S16 #03-09
Speaker : Bao Huanchen, National University of Singapore

Date/Time:02 Oct 2019 10:00 Venue: S16 #03-09 Speaker: Bao Huanchen, National University of Singapore The m=2 amplituhedron An amplituhedron (defined in terms of totally nonnegative Grassmannians) is a geometric structure introduced in 2013 by two physicists Nima Arkani-Hamed and Jaroslav Trnka. In this talk I shall explain the triangulation of the m=2 amplituhedron. This is joint work with Xuhua He. Add to calendar: 

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