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Organizing Committee

John Cremona
University of Warwick

Kiran Kedlaya
University of California, San Diego

Ralf Schmidt
University of Oklahoma

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.

Modular Forms and Curves of Low Genus: Computational Aspects

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Lecture Videos

Elliptic Curves with Good Reduction Outside S

Angelos Koutsianas

Ulm University

September 28, 2015 • 12:00 AM

Modular Forms and Curves of Low Genus: Computational Aspects

Modular Forms and Curves of Low Genus: Computational Aspects

Sep 28 - Oct 2, 2015

Organizing Committee

Abstract

Lecture Videos

Elliptic Curves with Good Reduction Outside S

Constructing genus 2 curves over finite fields

Isogenies, polarisations and real multiplication

Genus two CM curves and their invariants

Variations on quadratic Chabauty

Genus 3 curves and the inverse Galois problem

Shimura Degrees, New Modular Degrees, and Congruence Primes

Non-archimedean construction of elliptic curves and abelian surfaces

Tables of paramodular eigenforms

Modularity of the abelian surface of conductor 277

Experimental results for Siegel modular forms

Quadratic twists of Siegel modular forms of paramodular level- motivation a...

Quadratic twists of Siegel modular forms of paramodular level- Hecke operat...

Explicit methods in the theory of Jacobi forms of lattice index and over nu...

A survey on the modularity of abelian surfaces

On the paramodular conjecture

Computing the images of Galois representations

Computing L-series of hyperelliptic curves in moderate genus

Local Galois representations and stable reduction of curves

Constructing genus 3 hyperelliptic Jacobians - a mathematician's point of v...

Constructing genus 3 hyperelliptic Jacobians with CM - a cryptographer's po...

Obtaining modular units via a recurrence relation

Associated Semester Workshops

Computational Aspects of the Langlands Program

Explicit Methods for Modularity of K3 Surfaces and Other Higher Weig...

Computational Aspects of L-functions

Modular Forms and Curves of Low Genus: Computational Aspects

Sep 28 - Oct 2, 2015

Organizing Committee

Abstract

Confirmed Speakers & Participants

Lecture Videos

Elliptic Curves with Good Reduction Outside S

Constructing genus 2 curves over finite fields

Isogenies, polarisations and real multiplication

Genus two CM curves and their invariants

Variations on quadratic Chabauty

Genus 3 curves and the inverse Galois problem

Shimura Degrees, New Modular Degrees, and Congruence Primes

Non-archimedean construction of elliptic curves and abelian surfaces

Tables of paramodular eigenforms

Modularity of the abelian surface of conductor 277

Experimental results for Siegel modular forms

Quadratic twists of Siegel modular forms of paramodular level- motivation a...

Quadratic twists of Siegel modular forms of paramodular level- Hecke operat...

Explicit methods in the theory of Jacobi forms of lattice index and over nu...

A survey on the modularity of abelian surfaces

On the paramodular conjecture

Computing the images of Galois representations

Computing L-series of hyperelliptic curves in moderate genus

Local Galois representations and stable reduction of curves

Constructing genus 3 hyperelliptic Jacobians - a mathematician's point of v...

Constructing genus 3 hyperelliptic Jacobians with CM - a cryptographer's po...

Obtaining modular units via a recurrence relation

Associated Semester Workshops

Computational Aspects of the Langlands Program

Explicit Methods for Modularity of K3 Surfaces and Other Higher Weig...

Computational Aspects of L-functions

Confirmed Speakers & Participants