Organizing Committee
 John Cremona
University of Warwick  Kiran Kedlaya
University of California, San Diego  Kristin Lauter
Microsoft  Ralf Schmidt
University of Oklahoma  Joseph Silverman
Brown University
Abstract
One of the crowning achievements of number theory in the 20th century is the construction of the modularity correspondence between elliptic curves with rational coefficients and modular forms of weight 2. The consequences of this result resound throughout number theory; for instance, it enables the resolution of certain problems of diophantine equations (e.g., Fermat's last theorem) as well as the systematic tabulation of elliptic curves, which in turn provides the basis for many new conjectures and results.
The aim of this workshop is to lay the groundwork for extending this correspondence to curves of small genus over number fields. The general framework for this correspondence is predicted by the Langlands program, but much remains to be made explicit. We will explore theoretical, algorithmic, computational, and experimental questions on both sides of the correspondence, with an eye towards tabulation of numerical data and formulation of precise conjectures.
Confirmed Speakers & Participants

Dan Abramovich
Brown University

Samuele Anni
University of Warwick

Sonny Arora
The Pennsylvania State University

Jennifer Balakrishnan
University of Oxford

Olga Balkanova
ICERM

Cristina Ballantine
College of the Holy Cross

Dianbin Bao
Temple University

Michael Bennett
University of British Columbia

Sandro Bettin
Université de Montréal

Irene Bouw
Universität Ulm

Benjamin Breen
Dartmouth College

Reinier Bröker
Brown University

Armand Brumer
Fordham University

Alina Bucur
UCSD

Gregory Call
Amherst College

Marta Canadell
Georgia Institute of Technology

Marco Caselli
University of Warwick

Hao Chen
University of Washington

William Chen
Pennsylvania State University

John Conrey
American Institute of Mathematics

John Cremona
University of Warwick

John Cullinan
Bard College

Alyson Deines
Center for Communications Research

Lassina Dembele
Warwick University

Tim Dokchitser
University of Bristol

Valerio Dose
INdAM  Istituto Nazionale di Alta Matematica

Taylor Dupuy
The Hebrew University

Kirsten Eisentraeger
Pennsylvania State University

Ozlem Ejder
University of Southern California

David Farmer
AIM

Luis Finotti
University Of Tennessee

Francesc Fité
Universität DuisburgEssen

Sharon Frechette
College of the Holy Cross

Edray Goins
Purdue University

Benedict Gross
Harvard University

Lucio Guerberoff
University College London

David Harvey
University of New South Wales

Brendan Hassett
ICERM/Brown University

Ghaith Hiary
The Ohio State University

Sorina Ionica
University of Bordeaux

Jennifer JohnsonLeung
University of Idaho

John Jones
Arizona State University

Kiran Kedlaya
University of California, San Diego

Kamal KhuriMakdisi
American University of Beirut

Pinar Kilicer
Leiden University

Seoyoung Kim
Brown University

Daniel Kohen
University of Buenos Aires

Angelos Koutsianas
Ulm University

Sally Koutsoliotas
Bucknell University

Kenneth Kramer
CUNY

Watson Ladd
UC Berkeley

Kristin Lauter
Microsoft

TingFang Lee
Brown University

Wenching Li
Pennsylvania State University

Ling Long
Lousiana State University

Elisa Lorenzo Garcia
Universiteit Leiden

Kimball Martin
University of Oklahoma

Chloe Martindale
Leiden University

Edgar Martins Dias Costa
ICERM/Dartmouth College

Jolanta Marzec
University of Bristol

Nicolas Mascot
University of Warwick

Marc Masdeu
University of Warwick

Kathrin Maurischat
Heidelberg University

Anna Medvedovsky
ICERM

Rachel Newton
Institut Des Hautes Études Scientifiques (IHÉS)

Ariel Pacetti
University of Buenos Aires

Aurel Page
University of Warwick

Mihran Papikian
Pennsylvania State University

Ameya Pitale
University of Oklahoma

Damien Robert
INRIA

Brooks Roberts
University of Idaho

David Roberts
University of Minnesota, Morris

Michael Rubinstein
University of Waterloo

Nathan Ryan
Bucknell University

Samuel Schiavone
Dartmouth College

Ralf Schmidt
University of Oklahoma

Alok Shukla
University of Oklahoma

Jeroen Sijsling
Dartmouth College

Joseph Silverman
Brown University

Nils Skoruppa
Universität Siegen

Eduardo Soto Ballesteros
University of Barcelona

Marco Streng
Universiteit Leiden

Peng Sun
Central University of Finance and Economics

Andrew Sutherland
Massachusetts Institute of Technology

Holly Swisher
Oregon State University

Long Tran
University of Oklahoma

Nicholas Triantafillou
MIT

Christelle Vincent
University of Vermont

John Voight
Dartmouth College

Siddhesh Wagh
University of Oklahoma

James Weigandt
Purdue University

Stefan Wewers
Universität Ulm

Tonghai Yang
University of Wisconsin

David Yuen
Lake Forest College

David Zywina
Cornell University