Date/Time : 21 Jan 2020 14:00
Venue : S17 #04-06 SR1
Speaker : Ma Jiajun, Shanghai Jiao Tong University

Date/Time:21 Jan 2020 14:00 Venue: S17 #04-06 SR1 Speaker: Ma Jiajun, Shanghai Jiao Tong University Towards the explicit description of local descent of symplectic supercuspidal representations of GL(2n) Descent is the “inverse” of Langlands functorial lift. The descent of symplectic supercuspidal representations of GL(2n) to SO(2n+1) over p-adic fields was established by Dihua Jiang, Chufeng Nien, and Yujun Qin. In this talk, I will first give an explicit description of the local descent in the depth zero cases. Then I will discuss a conjectural description in the general case. This is ongoing joint work with Dongwen Liu, Chufeng Nien, and Zhicheng Wang. Add to calendar: 

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Date/Time : 21 Jan 2020 09:00
Venue : S17 #04-06 SR1
Speaker : Paul Nelson, ETH Zurich

Date/Time:21 Jan 2020 09:00 Venue: S17 #04-06 SR1 Speaker: Paul Nelson, ETH Zurich Quantum variance of compact arithmetic surfaces I will talk about the quantum variance of Hecke–Maass cusp forms on arithmetic hyperbolic surfaces. In the case of the non-compact modular surface, the asymptotic quantum variance was determined in work of Luo–Sarnak, Zhao and Sarnak–Zhao, using a method specific to that case. I will describe analogous results in the compact case, obtained by a different method based on the theta correspondence. This will involve some discussion of constructing microlocal lifts via convolution operators, identities and asymptotics involving integrals of theta functions, the Rallis inner product formula, and the method of coadjoint orbits. Add to calendar: 

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Date/Time : 15 Jan 2020 15:30
Venue : S17 #04-04 SR3
Speaker : Qi Zhi, Zhejiang University

Date/Time:15 Jan 2020 15:30 Venue: S17 #04-04 SR3 Speaker: Qi Zhi, Zhejiang University A Bessel delta-method and its applications In this talk, I will introduce a new $\delta$-method by a certain Bessel integral and its applications in the theory of exponential sums for $GL(2)$. In particular, it gives a simple proof of the Weyl-type subconvex bound for modular form $L$-functions in the $t$-aspect. This is joint work with Aggarwal, Holowinksy and Lin. Add to calendar: 

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Date/Time : 10 Dec 2019 14:00
Venue : S17 #04-04 SR3
Speaker : Cheng-Chiang Tsai, Stanford University

Date/Time:10 Dec 2019 14:00 Venue: S17 #04-04 SR3 Speaker: Cheng-Chiang Tsai, Stanford University Local Langlands and character sheaves Let G be a connected reductive group and G^{\vee} be its dual group. For example, G=SO_{2n+1} and G^{\vee}=Sp_{2n} the symplectic group on a 2n-dimensional space. The Langlands correspondence can be interpreted as attaching monodromies to representations. Over a local or global field, to certain representation one can attach a Galois representation (or some variant of it), in other words monodromic datum over the field. While local/global Langlands is largely mysterious, over a finite field there is the Deligne-Lusztig theory and theory of character sheaves; to each irreducible representation of G(F_q) or character sheaf on G one can attache a monodromy as a semisimple element in G^{\vee}. This finite field picture is completely established by Lusztig. In this talk, we survey three seemingly unrelated connections between the local picture (in depth-zero case) and the finite field picture, raising new questions and proposing new conjectures. There will be no theorem in this talk. 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

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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