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Combinatorics, Multiple Dirichlet Series and Analytic Number Theory (April 15 - 19, 2013)


Organizing Committee

Description

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

  • Razia Amzad
    (Springer)
  • Johan Andersson
    (University of Stockholm)
  • Julio Cesar Andrade
    (University of Bristol)
  • Cristina Ballantine *
    (College of the Holy Cross)
  • Elizabeth Beazley
    (Haverford College)
  • Jennifer Beineke
    (Western New England University)
  • Arkady Berenstein
    (University of Oregon)
  • Valentin Blomer *
    (University of Goettingen)
  • Reinier Bröker
    (Brown University)
  • Benjamin Brubaker
    (Massachusetts Institute of Technology)
  • Daniel Bump
    (Stanford University)
  • Vyjayanthi Chari
    (University of California, Riverside)
  • Tapas Chatterjee
    (Institute of Mathematical Sciences)
  • Gautam Chinta
    (City College, CUNY)
  • Peter Cho
    (University of Toronto)
  • Youn-Seo Choi
    (Korea Institute for Advanced Study (KIAS))
  • Young Ju Choie*
    (Pohang University of Science and Technology (POSTECH))
  • Kwangho Choiy
    (Oklahoma State University)
  • Brian Conrey *
    (American Institute of Mathematics)
  • Zajj Daugherty
    (Dartmouth College)
  • Amy DeCelles
    (Goshen College)
  • Mario DeFranco
    (Massachusetts Institute of Technology)
  • Adrian Diaconu
    (University of Minnesota)
  • Nikos Diamantis*
    (University of Nottingham)
  • Gabriel Feinberg
    (University of Connecticut)
  • Sharon Frechette *
    (College of the Holy Cross)
  • Solomon Friedberg
    (Boston College)
  • Holley Friedlander
    (University of Massachusetts)
  • Howard Garland
    (Yale University)
  • Paul Garrett *
    (University of Minnesota)
  • Hunduma Legesse Geleta
    (Addis Ababa University)
  • Dorian Goldfeld
    (Columbia University)
  • Leo Goldmakher
    (University of Toronto)
  • Paul Gunnells
    (University of Massachusetts)
  • Jeffrey Hoffstein
    (Brown University)
  • Thomas Hulse
    (Brown University)
  • Joseph Hundley
    (Southern Illinois University)
  • Özlem Imamoḡlu
    (Swiss Federal Institute of Technology)
  • Bogdan Ion
    (University of Pittsburgh)
  • Cihan Karabulut
    (City University of New York (CUNY))
  • Henry Kim
    (University of Toronto)
  • Eren Kiral
    (Brown University)
  • Chan Ieong Kuan
    (Brown University)
  • Thomas Lam
    (University of Michigan)
  • Martina Lanini
    (University of Melbourne)
  • Kyu-Hwan Lee
    (University of Connecticut)
  • Min Lee*
    (Brown University)
  • Ting-Fang Lee
    (National Taiwan University)
  • Winnie Li*
    (Pennsylvania State University)
  • Xiaoqing Li*
    (University at Buffalo (SUNY))
  • Li-Mei Lim
    (Brown University)
  • Sheng-Chi Liu
    (Texas A & M University)
  • David Lowry
    (Brown University)
  • Péter Maga
    (Hungarian Academy of Sciences (MTA))
  • Yves Martin
    (University of Chile)
  • Kohji Matsumoto*
    (Nagoya University)
  • Peter McNamara *
    (Stanford University)
  • Djordje Milicevic
    (Bryn Mawr College)
  • Stephen Miller*
    (Rutgers University)
  • Alejandro Morales
    (University of Quebec)
  • Dinakar Muthiah
    (Brown University)
  • Omer Offen*
    (Technion-Israel Institute of Technology)
  • Soichi Okada
    (Nagoya University)
  • Lukasz Pankowski
    (Adam Mickiewicz University)
  • Yoon Kyung Park
    (Korea Institute for Advanced Study (KIAS))
  • Vicentiu Pasol*
    (Institute of Mathematics "Simion Stoilow" of the Romanian Academy)
  • Manish Patnaik
    (University of Alberta)
  • Samuel Patterson
    (Georg-August-Universität zu Göttingen)
  • Laura Peskin
    (California Institute of Technology)
  • Ian Petrow
    (Stanford University)
  • Andrew Pollington
    (National Science Foundation)
  • Anna Puskas
    (Columbia University)
  • Zhi Qi
    (Ohio State University)
  • Arun Ram
    (University of Melbourne)
  • Martin Raum
    (ETH)
  • Michael Rubinstein
    (University of Waterloo)
  • Ben Salisbury
    (City College, CUNY)
  • Anne Schilling
    (University of California, Davis)
  • Travis Scrimshaw
    (University of California, Davis)
  • Jyoti Sengupta*
    (Tata Institute of Fundamental Research)
  • Xin Shen
    (University of Minnesota)
  • Takashi Taniguchi*
    (Kobe University)
  • Nicolas Templier *
    (Princeton University)
  • Nicolas Thiery
    (Université de Paris XI (Paris-Sud))
  • Frank Thorne
    (University of South Carolina)
  • Ruoguang (Roger) Tian
    (University of California, Davis)
  • Vidya Venkateswaran
    (Massachusetts Institute of Technology)
  • Aladin Virmaux
    (Université de Paris XI (Paris-Sud))
  • Masato Wakayama
    (Kyushu University)
  • Xin Wang
    (University of Minnesota)
  • Jun Wen
    (Stony Brook University)
  • Ian Whitehead
    (Columbia University)
  • Siman Wong
    (University of Massachusetts)
  • Jae-Hyun Yang
    (Inha University)
  • Yangbo Ye*
    (University of Iowa)
  • Zhilin Ye
    (Ohio State University)
  • Lei Zhang *
    (Boston College)
  • Qiao Zhang
    (Texas Christian University)
  • Yichao Zhang
    (University of Connecticut)
  • Fan Zhou
    (Columbia University)
DatesTitleOrganizers
April 15 - 19, 2013Combinatorics, Multiple Dirichlet Series and Analytic Number TheoryGautam Chinta, Adrian Diaconu, Dorian Goldfeld, Ozlem Imamoglu

Workshop Video Links
Description Speaker
Video
Abstract
Slides
MondayApril 15, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:45Random Matrix theory and the zeros of the Riemann zeta-functionBrian Conrey, American Institute of Mathematics11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15A converse theorem for Dirichlet series in two variables and Shintani zeta functionsNikolaos Diamantis, University of Nottingham11th Floor Lecture Hall
PDF
11:30 - 12:15Discussion time11th Floor Lecture Hall
12:30 - 2:30Break for Lunch and Free Time
1:00 - 2:20Representations of affine Kac-Moody groups over local and global fields (ongoing semester course)Alexander Braverman, Brown University11th Floor Lecture Hall
2:45 - 3:30Self-adjoint operators on spaces of automorphic formsPaul Garrett, University of Minnesota11th Floor Lecture Hall
PDF
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:15 - 5:00Bounds for integrals of Jacquet-Whittaker functionsXiaoqing Li, University at Buffalo (SUNY)11th Floor Lecture Hall
PDF
5:00 - 6:30Welcome Reception11th Floor Collaborative Space

TuesdayApril 16, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Wellhausen's conjecture - what is it trying to tell usSamuel James Patterson, Georg-August-Universitat zu Gottingen11th Floor Lecture Hall
PDF
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Understanding the Chinta-Gunnells actionPeter McNamara, Stanford University11th Floor Lecture Hall
PDF
11:30 - 12:15The Iwahori-Hecke Algebra, the Ramanujan Conjecture, and Expander GraphsCristina Ballantine, College of the Holy Cross11th Floor Lecture Hall
PDF
PDF
12:30 - 12:35Group Photo11th Floor Lecture Hall
12:35 - 2:30Break for Lunch and Free Time
2:30 - 3:15Orbital L-functions for the space of binary cubic forms and their applicationsTakashi Taniguchi, Kobe University11th Floor Lecture Hall
PDF
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Second Moments and Shifted Multiple Dirichlet SeriesMin Lee, Brown University11th Floor Lecture Hall
PDF

WednesdayApril 17, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Hyperbolic Kac-Moody algebras and automorphic formsKyu-Hwan Lee, University of Connecticut11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Eisenstein Series on Covers of Odd Orthogonal GroupsLei Zhang, Boston College11th Floor Lecture Hall
PDF
11:30 - 12:15Discussion time11th Floor Lecture Hall
12:30 - 2:30Break for Lunch and Free Time
1:00 - 2:20Representations of affine Kac-Moody groups over local and global fields (ongoing semester course)Alexander Braverman, Brown University11th Floor Lecture Hall
2:30 - 3:15On the Fourier coefficients of elliptic modular forms of half-integral weightYoungJu Choie, Pohang University of Science and Technology (POSTECH)11th Floor Lecture Hall
PDF
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Period integrals of automorphic formsOmer Offen, Technion-Israel Institute of Technology11th Floor Lecture Hall
PDF
PDF
7:00 - 8:30Poster Session and Dessert Reception11th Floor Lecture Hall and Collaborative Space
PDF

ThursdayApril 18, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Entire continuation of cuspidal loop Eisenstein series.Stephen Miller, Rutgers University11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15On Higher Moments for Quadratic Dirichlet L-FunctionsVicentiu Pasol, Institute of Mathematics "Simion Stoilow" of the Romanian Academy11th Floor Lecture Hall
11:30 - 12:15The zeta-function of the root system of type G_2Kohji Matsumoto, Nagoya University11th Floor Lecture Hall
PDF
12:30 - 2:30Break for Lunch and Free Time
2:30 - 3:15Atkin and Swinnerton-Dyer congruences for noncongruence modular formsWinnie Li, Pennsylvania State University11th Floor Lecture Hall
PDF
PDF
3:20 - 3:30Please remember to fill out your survey. Paper copies available at the 11th floor reception desk.
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Harmonic families of automorphic representationsNicolas Templier, Princeton University11th Floor Lecture Hall
PDF

FridayApril 19, 2013
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 9:45Zero density for automorphic L-functionsYangbo Ye, University of Iowa11th Floor Lecture Hall
PDF
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:15Rational points on a cubic fourfoldValentin Blomer, University of Goettingen11th Floor Lecture Hall
PDF
11:30 - 12:15On effective determination of Maass forms from central values of Rankin-Selberg L functions.Jyoti Sengupta, Tata Institute of Fundamental Research11th Floor Lecture Hall
PDF
12:30 - 2:30Break for Lunch and Free Time
2:30 - 3:15Discussion time11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Discussion time11th Floor Lecture Hall