Organizing Committee
Abstract

Recent years have seen a flurry of activity in the field of Weyl group multiple Dirichlet series. Surprising and unexpected connections between these multiple Dirichlet series and several different fields of mathematics have emerged. This workshop will survey recent results and set the stage for future developments which further interrelate analytic number theory, automorphic forms and combinatorial representation theory.

Particular focus will be given to applications of Weyl group multiple Dirichlet series to the following areas:

  • Average value and nonvanishing results for families of L-functions
  • Periods of automorphic forms
  • Connections between characters sums over function fields and characters of affine root systems
  • Metaplectic Casselman-Shalika formulae and deformations of the Weyl character formula
    •

Image for "Combinatorics, Multiple Dirichlet Series and Analytic Number Theory"

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, April 15, 2013
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am EDTRandom Matrix theory and the zeros of the Riemann zeta-function - Brian Conrey, American Institute of Mathematics11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space  
10:30 - 11:15am EDTA converse theorem for Dirichlet series in two variables and Shintani zeta functions - Nikolaos Diamantis, University of Nottingham11th Floor Lecture Hall
11:30 - 12:15pm EDTDiscussion time11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
1:00 - 2:20pm EDTRepresentations of affine Kac-Moody groups over local and global fields (ongoing semester course) - Alexander Braverman, Brown University11th Floor Lecture Hall 
2:45 - 3:30pm EDTSelf-adjoint operators on spaces of automorphic forms - Paul Garrett, University of Minnesota11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:15 - 5:00pm EDTBounds for integrals of Jacquet-Whittaker functions - Xiaoqing Li, University at Buffalo (SUNY)11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, April 16, 2013
TimeEventLocationMaterials
9:00 - 9:45am EDTWellhausen's conjecture - what is it trying to tell us - Samuel James Patterson, Georg-August-Universitat zu Gottingen11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTUnderstanding the Chinta-Gunnells action - Peter McNamara, Stanford University11th Floor Lecture Hall
11:30 - 12:15pm EDTThe Iwahori-Hecke Algebra, the Ramanujan Conjecture, and Expander Graphs - Cristina Ballantine, College of the Holy Cross11th Floor Lecture Hall
12:30 - 12:35pm EDTGroup Photo11th Floor Lecture Hall 
12:35 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:15pm EDTOrbital L-functions for the space of binary cubic forms and their applications - Takashi Taniguchi, Kobe University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTSecond Moments and Shifted Multiple Dirichlet Series - Min Lee, Brown University11th Floor Lecture Hall
Wednesday, April 17, 2013
TimeEventLocationMaterials
9:00 - 9:45am EDTHyperbolic Kac-Moody algebras and automorphic forms - Kyu-Hwan Lee, University of Connecticut11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTEisenstein Series on Covers of Odd Orthogonal Groups - Lei Zhang, Boston College11th Floor Lecture Hall
11:30 - 12:15pm EDTDiscussion time11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
1:00 - 2:20pm EDTRepresentations of affine Kac-Moody groups over local and global fields (ongoing semester course) - Alexander Braverman, Brown University11th Floor Lecture Hall 
2:30 - 3:15pm EDTOn the Fourier coefficients of elliptic modular forms of half-integral weight - YoungJu Choie, Pohang University of Science and Technology (POSTECH)11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTPeriod integrals of automorphic forms - Omer Offen, Technion-Israel Institute of Technology11th Floor Lecture Hall
7:00 - 8:30pm EDTPoster Session and Dessert Reception11th Floor Lecture Hall and Collaborative Space 
Thursday, April 18, 2013
TimeEventLocationMaterials
9:00 - 9:45am EDTEntire continuation of cuspidal loop Eisenstein series. - Stephen Miller, Rutgers University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTOn Higher Moments for Quadratic Dirichlet L-Functions - Vicentiu Pasol, Institute of Mathematics "Simion Stoilow" of the Romanian Academy11th Floor Lecture Hall 
11:30 - 12:15pm EDTThe zeta-function of the root system of type G_2 - Kohji Matsumoto, Nagoya University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:15pm EDTAtkin and Swinnerton-Dyer congruences for noncongruence modular forms - Winnie Li, Pennsylvania State University11th Floor Lecture Hall
3:20 - 3:30pm EDTPlease remember to fill out your survey. Paper copies available at the 11th floor reception desk.  
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTHarmonic families of automorphic representations - Nicolas Templier, Princeton University11th Floor Lecture Hall
Friday, April 19, 2013
TimeEventLocationMaterials
9:00 - 9:45am EDTZero density for automorphic L-functions - Yangbo Ye, University of Iowa11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTRational points on a cubic fourfold - Valentin Blomer, University of Goettingen11th Floor Lecture Hall
11:30 - 12:15pm EDTOn effective determination of Maass forms from central values of Rankin-Selberg L functions. - Jyoti Sengupta, Tata Institute of Fundamental Research11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:15pm EDTDiscussion time11th Floor Lecture Hall 
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTDiscussion time11th Floor Lecture Hall 

Associated Semester Workshops

Lecture Videos

On effective determination of Maass forms from central values of Rankin-Selberg L functions.

Jyoti Sengupta
Tata Institute of Fundamental Research
April 19, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

Zero density for automorphic L-functions

Yangbo Ye
University of Iowa
April 19, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

Harmonic families of automorphic representations

Nicolas Templier
Princeton University
April 18, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

Atkin and Swinnerton-Dyer congruences for noncongruence modular forms

Wenching Li
Pennsylvania State University
April 18, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract     Slides

The zeta-function of the root system of type G 2

Kohji Matsumoto
Nagoya University
April 18, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract     Slides

On Higher Moments for Quadratic Dirichlet L-Functions

Vicentiu Pasol
Institute of Mathematics "Simion Stoilow" of the Romanian Academy
April 18, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play

Entire continuation of cuspidal loop Eisenstein series.

Stephen Miller
Rutgers University
April 18, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

Period integrals of automorphic forms

Omer Offen
Technion-Israel Institute of Technology
April 17, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract     Slides

On the Fourier coefficients of elliptic modular forms of half-integral weight

YoungJu Choie
POSTECH
April 17, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

Eisenstein Series on Covers of Odd Orthogonal Groups

Lei Zhang
Shanghai Jiao Tong University
April 17, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract     Slides

Hyperbolic Kac-Moody algebras and automorphic forms

Kyu-Hwan Lee
University of Connecticut
April 17, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

Orbital L-functions for the space of binary cubic forms and their applications

Takashi Taniguchi
Kobe University
April 16, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

The Iwahori-Hecke Algebra, the Ramanujan Conjecture, and Expander Graphs

Cristina Ballantine
College of the Holy Cross
April 16, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract     Slides

Understanding the Chinta-Gunnells action

Peter McNamara
Stanford University
April 16, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

Wellhausen's conjecture - what is it trying to tell us

Samuel Patterson
Georg-August-Universität zu Göttingen
April 16, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract     Slides

Bounds for integrals of Jacquet-Whittaker functions

Xiaoqing Li
University at Buffalo (SUNY)
April 15, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

Self-adjoint operators on spaces of automorphic forms

Paul Garrett
University of Minnesota
April 15, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

A converse theorem for Dirichlet series in two variables and Shintani zeta functions

Nikolas Diamantis
University of Nottingham
April 15, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract

Random Matrix theory and the zeros of the Riemann zeta-function

John Conrey
American Institute of Mathematics
April 15, 2013
Combinatorics, Multiple Dirichlet Series and Analytic Number Theory
Play     Abstract