Home /  Introductory Workshop: Diophantine Geometry

Workshop

Introductory Workshop: Diophantine Geometry February 06, 2023 - February 10, 2023
Registration Deadline: February 17, 2023 over 1 year ago
To apply for Funding you must register by: October 23, 2022 over 1 year ago
Parent Program:
Location: SLMath: Eisenbud Auditorium, Atrium
Organizers Hector Pasten (Pontificia Universidad Católica de Chile), Yunqing Tang (University of California, Berkeley), LEAD Shou-Wu Zhang (Princeton University)
Speaker(s)

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Description
Introd image
Rational points on a general type surface. Image by Hector Pasten.
This will be a hybrid workshop with both in-person and virtual participation. This workshop will feature expository lectures about  current developments in  Diophantine geometry. This includes  the uniform Mordell—Lang for rational points on curves,  the  Andre—Oort conjecture for special points on Shimura varieties, and effective results via Chabauty method, and related topics in  Arakelov theory, unlikely intersections, arithmetic statistics, arithmetic dynamics, and p-adic Hodge theory. Bibliography
Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • rational points

  • special points

  • Chabauty method

  • Arakelov theory

  • unlikely intersections

  • arithmetic statistics

  • arithmetic dynamics

  • p-adic Hodge theory

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics Show All Collapse

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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Feb 06, 2023
Monday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:30 AM
  Moduli Spaces for Dynamical Systems on Projective Space
Joseph Silverman (Brown University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  A Finite Index Conjecture for Iterated Galois Groups
Thomas Tucker (University of Rochester)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Heights of Rational Points on Stacks
Jordan Ellenberg (University of Wisconsin-Madison)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  On the Toric Locus of L-Adic Local Systems (Joint work with J. Stix)
Anna Cadoret (Sorbonne University)
Feb 07, 2023
Tuesday
09:30 AM - 10:30 AM
  On the Distribution of the Hodge Locus
Emmanuel Ullmo (IHES)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Some Effective Methods in the Context of the Mordell-Lang Conjecture
Evelina Viada (Universität Göttingen)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Sparsity of Rational and Algebraic Points
Ziyang Gao (Leibniz Universität Hannover)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  A Product Formula for Periods
Pierre Colmez (Institut de Mathématiques de Jussieu)
04:30 PM - 06:20 PM
  Reception
Feb 08, 2023
Wednesday
09:30 AM - 10:30 AM
  Heights in the Isogeny Class of an Abelian Variety
Mark Kisin (Harvard University)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Tate-Semisimplicity Over Finite Fields
Ananth Shankar (University of Wisconsin-Madison)
12:00 PM - 02:00 PM
  Lunch
03:00 PM - 03:30 PM
  Afternoon Tea
Feb 09, 2023
Thursday
09:30 AM - 10:30 AM
  The Filtration Method in Diophantine Geometry
Min Ru (University of Houston)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Modularity and Height Bounds
Hector Pasten (Pontificia Universidad Católica de Chile)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Quadratic Chabauty for Modular Curves
Jennifer Balakrishnan (Boston University)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Path Integrals and L-Functions
Minhyong Kim (International Centre for Mathematical Sciences)
Feb 10, 2023
Friday
09:30 AM - 10:30 AM
  Formal-Analytic Surfaces: Nori’s Bound in Arakelov Geometry and Archimedean Overflow
Jean-Benoit Bost (Faculté des Sciences d’Orsay)
10:30 AM - 11:00 AM
  Break
11:00 AM - 12:00 PM
  Formal-Analytic Arithmetic Surfaces: Finiteness Theorems, and Applications to Arithmetic Fundamental Groups
François Charles (École Normale Supérieure)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  Unlikely Intersections and Applications to Diophantine Problems
Laura Capuano (Università degli Studi Roma Tre)
03:00 PM - 03:30 PM
  Afternoon Tea
03:30 PM - 04:30 PM
  Polynomials with Squarefree Discriminant
Arul Shankar (University of Toronto)