Organizing Committee
Abstract

Only recently has it become feasible to do large scale verification of the predictions of the Langlands program in higher rank cases and to present the results in a way that is accessible widely to mathematicians. Moving from the understanding of Galois representations attached to elliptic curves to those attached to surfaces and other higher-dimensional varieties poses interesting problems in both arithmetic, algebra, geometry, and analysis.

In this workshop, we will consider computational and other explicit aspects of modular forms in higher rank. Topics covered will include: K3 surfaces and their connections to modular forms on orthogonal groups, algebraic modular forms associated to classical groups and their computation, and motives arising from general Calabi-Yau varieties accessible to explicit methods, including hypergeometric motives.

This workshop will bring together researchers who approach the Langlands program from a number of different perspectives, and our goal is to work in developing both the theoretical and computational aspects in tandem.

Confirmed Speakers & Participants

Workshop Schedule

Monday, October 19, 2015
TimeEventLocationMaterials
8:30 - 9:15Registration121 S.Main Street, Providence, RI (11th Floor Collaborative Space) 
9:15 - 9:25Welcome - ICERM Director11th Floor Lecture Hall 
9:30 - 10:15Modularity of K3 surfaces and Calabi-Yau threefolds - Matthias Schütt, Gottfried Wilhelm Leibniz Universität Hannover11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45From K3 surfaces to noncongruence modular forms - Wenching Li, Pennsylvania State University11th Floor Lecture Hall
12:00 - 2:00Break for Lunch  
2:00 - 2:45Calabi-Yau modular forms - Hossein Movasati, IMPA11th Floor Lecture Hall
3:00 - 3:30Coffee/Tea Break  
3:30 - 4:15Brauer groups of K3 surfaces and moduli of special cubic fourfolds - Anthony Varilly-Alvarado, Rice University11th Floor Lecture Hall
4:30 - 5:15Complete hypergeometric L-functions - David Roberts, University of Minnesota, Morris11th Floor Lecture Hall
5:30 - 7:00Welcome Reception11th Floor Collaborative Space 
Tuesday, October 20, 2015
TimeEventLocationMaterials
9:00 - 9:45Refining the Langlands correspondence for symplectic motives - Benedict Gross, Harvard University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Counting points on K3 surfaces- some complexity guesstimates - David Harvey, University of New South Wales11th Floor Lecture Hall
11:30 - 12:15more elementary evaluations of some K3 point-counts and periods - Noam Elkies, Harvard University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch  
2:30 - 3:15Effective computations of Hasse--Weil zeta functions - Edgar Costa, ICERM and Dartmouth College11th Floor Lecture Hall
3:30 - 4:15Point counting on K3 surfaces and applications - Andreas-Stephan Elsenhans, Universität Paderborn11th Floor Lecture Hall
4:30 - 6:00Poster Session/Coffee Break - 11th Floor Collaborative Space 
Wednesday, October 21, 2015
TimeEventLocationMaterials
9:00 - 10:00One parameter families of Calabi--Yau threefolds with trivial monodromy - Slawomir Cynk, Jagiellonian University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15K3 surfaces with real multiplication - Joerg Jahnel, University of Siegen11th Floor Lecture Hall
11:30 - 12:15Complex multiplication and K3 surfaces over finite fields - Lenny Taelman, University of Amsterdam11th Floor Lecture Hall
12:30 - 12:30Group Photo in Lecture Hall11th Floor Lecture Hall 
12:30 - 2:30Break for Lunch  
2:30 - 5:00Discussion/ Research/ Free Time  
3:30 - 4:00Coffee/Tea Break  
Thursday, October 22, 2015
TimeEventLocationMaterials
9:00 - 9:45Mirror symmetry and K3 surface zeta functions. - Ursula Whitcher, University of Wisconsin- Eau Claire11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Arithmetic Mirror Symmetry of K3 surfaces and Hypergeometric Functions - Adriana Salerno, Bates College11th Floor Lecture Hall
11:30 - 12:15Calabi–Yau threefolds of Borcea–Voisin type and Arithmetic Mirror Symmetry - Noriko Yui, Queen's University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch  
2:30 - 3:15Higher rank theta lifts and applications to modularity - Lassina Dembele, University of Warwick11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break  
4:00 - 4:45Moduli spaces of genus 2 curves with split Jacobians through K3 surfaces - Abhinav Kumar, Stony Brook University11th Floor Lecture Hall
Friday, October 23, 2015
TimeEventLocationMaterials
9:00 - 9:45Testing automorphicity of lifts of Hilbert modular forms - Clifton Cunningham, University of Calgary11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30Mordell-Weil group of isotrivial families of curves - Remke Kloosterman, Humboldt University of Berlin 
11:30 - 12:15Sato-Tate groups of higher weight motives - Kiran Kedlaya, UCSD11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break  

Associated Semester Workshops

Computational Aspects of the Langlands Program
Computational Aspects of L-functions

Lecture Videos