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Organizing Committee

Fernando Rodriguez-Villegas
University of Texas, Austin

Matthias Schuett
Gottfried Wilhelm Leibniz Universität Hannover

Holly Swisher
Oregon State University

Yuri Tschinkel
New York University

Bianca Viray
University of Washington

John Voight
Dartmouth College

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.

Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives

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Lecture Videos

Modularity of K3 surfaces and Calabi-Yau threefolds

Matthias Schuett

Gottfried Wilhelm Leibniz Universität Hannover

October 19, 2015 • 12:00 AM

Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives

Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives

Oct 19 - 24, 2015

Organizing Committee

Abstract

Lecture Videos

Modularity of K3 surfaces and Calabi-Yau threefolds

From K3 surfaces to noncongruence modular forms

Calabi-Yau modular forms

Counting points on K3 surfaces

Brauer groups of K3 surfaces and moduli of special cubic fourfold

Complete Hypergeometric L-functions

Elementary evaluations of some K3 point-counts and periods

Effective computations of Hasse--Weil zeta functions

Point counting on K3 surfaces and applications

One parameter families of Calabi--Yau threefolds with trivial monodromy

K3 surfaces with real multiplication

Arithmetic Mirror Symmetry of K3 surfaces and Hypergeometric Functions

Calabi-Yau threefolds of Borcea-Voisin type and Arithmetic Mirror Symmetry

Testing automorphicity of lifts of Hilbert modular forms

Mordell-Weil group of isotrivial families of curves

Sato-Tate groups of higher weight motives

Refining the Langlands correspondence for symplectic motives

Complex multiplication and K3 surfaces over finite fields

Mirror symmetry and K3 surface zeta functions.

Higher rank theta lifts and applications to modularity

Moduli spaces of genus 2 curves with split Jacobians through K3 surfaces

Associated Semester Workshops

Computational Aspects of the Langlands Program

Modular Forms and Curves of Low Genus: Computational Aspects

Computational Aspects of L-functions

Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives

Oct 19 - 24, 2015

Organizing Committee

Abstract

Confirmed Speakers & Participants

Lecture Videos

Modularity of K3 surfaces and Calabi-Yau threefolds

From K3 surfaces to noncongruence modular forms

Calabi-Yau modular forms

Counting points on K3 surfaces

Brauer groups of K3 surfaces and moduli of special cubic fourfold

Complete Hypergeometric L-functions

Elementary evaluations of some K3 point-counts and periods

Effective computations of Hasse--Weil zeta functions

Point counting on K3 surfaces and applications

One parameter families of Calabi--Yau threefolds with trivial monodromy

K3 surfaces with real multiplication

Arithmetic Mirror Symmetry of K3 surfaces and Hypergeometric Functions

Calabi-Yau threefolds of Borcea-Voisin type and Arithmetic Mirror Symmetry

Testing automorphicity of lifts of Hilbert modular forms

Mordell-Weil group of isotrivial families of curves

Sato-Tate groups of higher weight motives

Refining the Langlands correspondence for symplectic motives

Complex multiplication and K3 surfaces over finite fields

Mirror symmetry and K3 surface zeta functions.

Higher rank theta lifts and applications to modularity

Moduli spaces of genus 2 curves with split Jacobians through K3 surfaces

Associated Semester Workshops

Computational Aspects of the Langlands Program

Modular Forms and Curves of Low Genus: Computational Aspects

Computational Aspects of L-functions

Confirmed Speakers & Participants