Representation Theory and Number Theory Archives - Page 14 of 16

Seminars: Representation Theory and Number Theory

Date
Time
Venue

Speaker
Affiliation
Title of Talk

12 Feb 2020
10:00
S16 #03-04

Ma Jiajun
Shanghai Jiao Tong University
Cells and Primitive Ideals

Cells and Primitive Ideals

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:

Add to calendar :

05 Feb 2020
10:00
S17 #04-04 SR3

Bao Huanchen
NUS
Asymptotic Hecke algebras, part 2

Asymptotic Hecke algebras, part 2

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:

Add to calendar :

29 Jan 2020
10:00
S17 #04-04 SR3

Bao Huanchen
NUS
Asymptotic Hecke algebras, part 1

Asymptotic Hecke algebras, part 1

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:

Add to calendar :

21 Jan 2020
14:00
S17 #04-06 SR1

Ma Jiajun
Shanghai Jiao Tong University
Towards the explicit description of local descent of symplectic supercuspidal representations of GL(2n)

Towards the explicit description of local descent of symplectic supercuspidal representations of GL(2n)

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:

Add to calendar :

21 Jan 2020
09:00
S17 #04-06 SR1

Paul Nelson
ETH Zurich
Quantum variance of compact arithmetic surfaces

Quantum variance of compact arithmetic surfaces

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:

Add to calendar :

15 Jan 2020
15:30
S17 #04-04 SR3

Qi Zhi
Zhejiang University
A Bessel delta-method and its applications

A Bessel delta-method and its applications

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:

Add to calendar :

10 Dec 2019
14:00
S17 #04-04 SR3

Cheng-Chiang Tsai
Stanford University
Local Langlands and character sheaves

Local Langlands and character sheaves

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:

Add to calendar :

21 Nov 2019
10:00
S17 #04-06 SR1

Yao Cheng
Institute of Mathematics, Academia Sinica
On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions

On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions

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.

Add to calendar :

21 Nov 2019
10:00
S17 #04-06 SR1

Yao Cheng
Institute of Mathematics, Academia Sinica
On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions

On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions

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:

Add to calendar :