Organizing Committee
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


This workshop is an activity of the Simons Collaboration 'Arithmetic Geometry, Number Theory, and Computation' and is supported by the Simons Foundation.

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee

Workshop Schedule

Monday, June 3, 2019
TimeEventLocationMaterials
8:30 - 8:55Registration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:50Hearing algebraic curves and factoring polynomials - Felipe Voloch, University of Canterbury11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Local-global principles for endomorphism rings of abelian varieties - Davide Lombardo, Università di Pisa11th Floor Lecture Hall
11:35 - 12:25Endomorphisms and decompositions of Jacobians - Jeroen Sijsling, Universität Ulm11th Floor Lecture Hall
12:35 - 2:30Break for Lunch / Free Time  
2:30 - 3:20Decomposing Jacobian Varieties - Jen Paulhus, Grinnell College11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50Arithmetic of hyperelliptic curves over local fields - Celine Maistret, Boston University11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, June 4, 2019
TimeEventLocationMaterials
9:00 - 9:50On uniformity conjectures for abelian varieties and K3 surfaces over number fields - Yuri Zarhin, Pennsylvania State University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Low degree points on curves - Isabel Vogt, Stanford University11th Floor Lecture Hall
11:35 - 12:25Abelian Divisibility Sequences - Joe Silverman, Brown University11th Floor Lecture Hall
12:35 - 2:30Break for Lunch / Free Time  
2:30 - 3:30Lightning Talks Session 111th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00Lightning Talks Session 211th Floor Lecture Hall
Wednesday, June 5, 2019
TimeEventLocationMaterials
9:00 - 9:50Prym varieties of genus four curves - Nils Bruin, Simon Fraser University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Sato-Tate groups of abelian threefolds - Francesc Fité, IAS11th Floor Lecture Hall
11:35 - 12:25Problem Session11th Floor Lecture Hall
12:35 - 12:40Group Photo11th Floor Lecture Hall 
12:40 - 3:30Break for Lunch / Free Time  
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50Free Time11th Floor Lecture Hall 
Thursday, June 6, 2019
TimeEventLocationMaterials
9:00 - 9:50Counting isogenous principally-polarized abelian varieties over finite fields - Everett Howe, Center for Communications Research, La Jolla11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Arithmetic of twists of supersingular abelian varieties - Valentijn Karemaker, University of Pennsylvania11th Floor Lecture Hall
11:35 - 12:25Newton Polygon Stratification of the Torelli Locus in PEL-type Shimura Varieties - Wanlin Li, University of Wisconsin-Madison11th Floor Lecture Hall
12:35 - 2:30Break for Lunch / Free Time  
2:30 - 3:20Using Abelian Varieties for Multiparty non-Interactive Key Exchange - Alice Silverberg, University of California, Irvine11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50 Advances in Isogeny-based Cryptography - Benjamin Smith, Inria and École Polytechnique11th Floor Lecture Hall
Friday, June 7, 2019
TimeEventLocationMaterials
9:00 - 9:50Clutching of curves, Newton polygons, and unlikely intersections. - Rachel Pries, Colorado State University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Abelian varieties with everywhere good reduction over certain real quadratic fields of small discriminant - Lassina Dembele, Dartmouth College11th Floor Lecture Hall
11:35 - 12:25Exceptional Vinberg representations and moduli spaces - Eric Rains, California Institute of Technology11th Floor Lecture Hall
12:35 - 2:30Break for Lunch / Free Time  

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Lecture Videos

Advances in Isogeny-based Cryptography

Benjamin Smith
Inria and École Polytechnique
June 6, 2019

Endomorphisms and decompositions of Jacobians

Jeroen Sijsling
Universität Ulm at the Institut für Reine Mathematik
June 3, 2019