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Organizing Committee

Jennifer Balakrishnan
Boston University

Noam Elkies
Harvard University

Brendan Hassett
ICERM/Brown University

John Voight
Dartmouth College

Abstract

In this workshop, we will explore a number of themes in the arithmetic of abelian varieties of low dimension (typically dimension 2–4), with a focus on computational aspects. Topics will include the study of torsion points, Galois representations, endomorphism rings, Sato-Tate distributions, Mumford-Tate groups, complex and p-adic analytic aspects, L-functions, rational points, and so on. We also seek to classify and tabulate these objects, in particular to understand explicitly the underlying moduli spaces (with specified polarization, endomorphism, and torsion structure), and to find examples of abelian varieties exhibiting special behavior. Finally, we will pursue connections with related areas, including the theory of modular forms, related algebraic varieties (e.g., K3 surfaces), and special values of L-functions.

Our goal is for the workshop to bring together researchers working on abelian varieties in a number of facets to establish collaborations, develop algorithms, and stimulate further research.

Questions proposed in the workshop problem session

Arithmetic of Low-Dimensional Abelian Varieties

This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.

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Lecture Videos

Hearing algebraic curves and factoring polynomials

Jose Voloch

University of Canterbury

June 3, 2019 • 12:00 AM

Arithmetic of Low-Dimensional Abelian Varieties

Jun 3 - 7, 2019

Organizing Committee

Abstract

Lecture Videos

Hearing algebraic curves and factoring polynomials

Local-global principles for endomorphism rings of abelian varieties

Endomorphisms and decompositions of Jacobians

Decomposing Jacobian Varieties

Arithmetic of hyperelliptic curves over local fields

On uniformity conjectures for abelian varieties and K3 surfaces over number...

Low degree points on curves

Abelian Divisibility Sequences

Prym varieties of genus four curves

Sato-Tate groups of abelian threefolds

Counting isogenous principally-polarized abelian varieties over finite fiel...

Arithmetic of twists of supersingular abelian varieties

Newton Polygon Stratification of the Torelli Locus in PEL-type Shimura Vari...

Advances in Isogeny-based Cryptography

Clutching of curves, Newton polygons, and unlikely intersections

Abelian varieties with everywhere good reduction over certain real quadrati...

Exceptional Vinberg representations and moduli spaces

Arithmetic of Low-Dimensional Abelian Varieties

Jun 3 - 7, 2019

Organizing Committee

Abstract

Confirmed Speakers & Participants

Lecture Videos

Hearing algebraic curves and factoring polynomials

Local-global principles for endomorphism rings of abelian varieties

Endomorphisms and decompositions of Jacobians

Decomposing Jacobian Varieties

Arithmetic of hyperelliptic curves over local fields

On uniformity conjectures for abelian varieties and K3 surfaces over number...

Low degree points on curves

Abelian Divisibility Sequences

Prym varieties of genus four curves

Sato-Tate groups of abelian threefolds

Counting isogenous principally-polarized abelian varieties over finite fiel...

Arithmetic of twists of supersingular abelian varieties

Newton Polygon Stratification of the Torelli Locus in PEL-type Shimura Vari...

Advances in Isogeny-based Cryptography

Clutching of curves, Newton polygons, and unlikely intersections

Abelian varieties with everywhere good reduction over certain real quadrati...

Exceptional Vinberg representations and moduli spaces

Confirmed Speakers & Participants