ICERM Semester Program on "Computational Aspects of the Langlands Program"
(September 9, 2015 - December 4, 2015)

[Photo Credit: John Voight]

Introduction

In the late 1960s, Robert Langlands discovered a unifying principle in number theory providing a vast generalization of class field theory to include nonabelian extensions of number fields. This principle gives rise to a web of conjectures called the Langlands program which continues to guide research in number theory to the present day. For example, an important first instance of the Langlands program is the modularity theorem for elliptic curves over the rational numbers, an essential ingredient in the proof of Fermat's last theorem.

Despite its many successes, the Langlands program remains vague in many of its predictions, due in part to an absence of data to guide a precise formulation away from a few special cases. In this thematic program, we will experiment with and articulate refined conjectures relating arithmetic-geometric objects to automorphic forms, improve the computational infrastructure underpinning the Langlands program, and assemble additional supporting data. Such data has proven valuable for researchers in number theory, and it will continue to be made available at the L-Functions and Modular Forms Database.

During the semester we will focus on three specific aspects of the Langlands program. First, we will look at elliptic curves over number fields and genus 2 curves over the rationals and will consider their relationship to modular forms. Second, we will consider computational aspects of modular forms in higher rank. Specifically, we will examine K3 surfaces and their connections to modular forms on orthogonal groups. Our third topic concerns analytic aspects of L-functions, building upon and complementing the algebraic, arithmetic, and geometric data.

Organizing Committee

  • Alina Bucur
    (UCSD)
  • Brian Conrey
    (AIM and University of Bristol)
  • David Farmer
    (AIM)
  • John Jones
    (Arizona State University)
  • Kiran Kedlaya
    (UCSD)
  • Michael Rubinstein
    (University of Waterloo)
  • Holly Swisher
    (Oregon State University)
  • John Voight
    (Dartmouth College)

Associated Events & Information

Fall 2015 Semester Workshops

DatesTitleOrganizers
September 28 - October 2, 2015Modular Forms and Curves of Low Genus: Computational Aspects John Cremona, Kiran Kedlaya, Kristin Lauter, Ralf Schmidt, Joseph Silverman
October 19-23, 2015Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives Matthias Schütt, Fernando Rodriguez-Villegas, Bianca Viray, Holly Swisher, Yuri Tschinkel, John Voight
November 9-13, 2015Computational Aspects of L-functions Valentin Blomer, Brian Conrey, Chantal David, David Farmer, Michael Rubinstein, Peter Sarnak

This page will show upcoming seminars that will be scheduled by organizers, speakers, and participants of the Fall 2015 semester program. Walk-ins are welcomed and encouraged for these seminars. Please check back regularly for updates.

We provide an iCal link for those attendees who wish to sync their own devices and/or calendars to our schedule.


Wednesday September 9, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 1:30Check-In121 S Main St, Providence, RI 02903, USA
1:45 - 2:00Opening WelcomeJill Pipher, ICERM Director11th Floor Lecture Hall
2:00 - 3:30Discussion: semester topics and goalsModerated by Alina Bucur, UCSD11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:30Discussion: set schedule for the semester11th Floor Lecture Hall
4:30 - 5:30Organizational meeting for seminars and minicourses11th Floor Lecture Hall
5:30 - 7:00Welcome Reception11th Floor Collaborative Space

Thursday September 10, 2015
Time Description Speaker Location Abstracts Slides
9:30 - 10:00Overview of the Langlands programKiran S. Kedlaya, UCSD11th Floor Lecture Hall
10:15 - 11:15Introduction to the LMFDBDavid Farmer, AIM11th Floor Lecture Hall
11:30 - 11:355-minute Graduate student introductionsBenjamin Breen, Dartmouth College11th Floor Lecture Hall
11:35 - 11:405-minute Graduate student introductionsWilliam Chen, Penn State11th Floor Lecture Hall
11:40 - 11:455-minute Graduate student introductionsZhou Fang, Brown University11th Floor Lecture Hall
11:45 - 11:505-minute Graduate student introductionsSeoyoung Kim, Brown University11th Floor Lecture Hall
11:50 - 11:555-minute Graduate student introductionsWatson Ladd, UC Berkeley11th Floor Lecture Hall
11:55 - 12:005-minute Graduate student introductionsDavid Lowry, Brown University11th Floor Lecture Hall
12:00 - 2:00Lunch and Free Time
2:00 - 3:00Introduction to automorphic formsRalf Schmidt, University of Oklahoma11th Floor Lecture Hall
3:00 - 3:055-minute Graduate student introductionsMichael Neururer, University of Nottingham11th Floor Lecture Hall
3:05 - 3:105-minute Graduate student introductionsJolanta Marzec, University of Bristol11th Floor Lecture Hall
3:10 - 3:155-minute Graduate student introductionsSamuel Schiavone, Dartmouth College11th Floor Lecture Hall
3:15 - 3:205-minute Graduate student introductionsAlok Shukla, University of Oklahoma11th Floor Lecture Hall
3:20 - 3:255-minute Graduate student introductionsLong Tran, University of Oklahoma11th Floor Lecture Hall
3:25 - 3:305-minute Graduate student introductionsAlexander Walker, Brown University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break
4:00 - 5:00What are motivesDavid Roberts, University of Minnesota - Morris11th Floor Lecture Hall

Friday September 11, 2015
Time Description Speaker Location Abstracts Slides
9:30 - 11:00Computational problems: the interesting vs the possibleAndrew Sutherland, MIT11th Floor Lecture Hall
11:00 - 12:00Introduction to computing complete number theoretic data: number fieldsJohn Jones, Arizona State University11th Floor Lecture Hall
12:00 - 2:00Lunch and Free Time
2:00 - 2:1010-minute Postdoc introductionOlga Balkanova, ICERM Semester Postdoc11th Floor Lecture Hall
2:10 - 2:2010-minute Postdoc introductionSandro Bettin, ICERM Semester Postdoc11th Floor Lecture Hall
2:20 - 2:3010-minute Postdoc introductionEdgar Costa, ICERM Semester Postdoc11th Floor Lecture Hall
2:30 - 2:4010-minute Postdoc introduction11th Floor Lecture Hall
2:40 - 2:5010-minute Postdoc introductionTingFang Lee, Brown University11th Floor Lecture Hall
2:50 - 3:0010 Minute Postdoc IntroductionsAnna Medvedovsky, ICERM Institute Postdoc11th Floor Lecture Hall
3:00 - 3:1010-minute Postdoc introductionJames Weingandt, ICERM Institute Postdoc11th Floor Lecture Hall
3:10 - 3:2010-minute Postdoc introductionMarta Canadell, ICERM Institute Postdoc11th Floor Lecture Hall
3:20 - 4:00Coffee/Tea Break
4:00 - 5:00L-functions: the glue that holds the world togetherBrian Conrey, AIM11th Floor Lecture Hall

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