Mathematics Research Communities

MRC Week 3, June 16-22, 2019

Explicit Methods in Arithmetic Geometry in Characteristic p


  • Renee Bell, University of Pennsylvania
  • Julia Hartmann, University of Pennsylvania
  • Valentijn Karemaker, University of Pennsylvania
  • Padmavathi Srinivasan, Georgia Institute of Technology
  • Isabel Vogt, Massachusetts Institute of Technology

The focus of this MRC will be on problems in arithmetic geometry over fields of positive characteristic p that are amenable to an explicit approach, including the construction of examples, as well as computational exploration. Compared to algebraic geometry in characteristic 0, studying varieties over fields of characteristic p comes with new challenges (such as the failure of generic smoothness and classical vanishing theorems), but also with additional structure (such as the Frobenius morphism and point-counts over finite fields) that can be exploited. This often leads to interesting arithmetic considerations: possible topics for the workshop include isogeny classes of abelian varieties over finite fields, Galois covers of curves and lifting problems, and arithmetic dynamics.

To reflect the inherent interdisciplinary nature of arithmetic geometry, we invite early-career mathematicians with a wide range of backgrounds in number theory, algebraic geometry, and other subjects that intersect these fruitfully, such as dynamics and commutative algebra. During the workshop, the participants will formulate and investigate open problems around areas of current interest in small collaborative groups. They will benefit from the mentorship of a diverse group of senior arithmetic geometers, and from activities tailored to junior researchers. For instance, there will be two problem brainstorming sessions (at the beginning and the end), expository talks on key techniques (such as recent computational advances), and career-related group discussions.

Participants in this MRC summer conference will have numerous opportunities to confer in person and virtually about their research problems with mathematicians who work in arithmetic geometry.


Throughout the week, three advisors will be on site:

  • Andrew Obus (Baruch College)
  • Bjorn Poonen (MIT)
  • Doug Ulmer (University of Arizona)

For two days each, three visiting advisors will be on site:

  • Daniel Krashen (University of Georgia)
  • Joseph Silverman (Brown University)
  • Christelle Vincent (University of Vermont)

Also, throughout the week via Skype, external advisors will be available for participant consultations:

  • Piotr Achinger (IMPAN)
  • Matt Baker (Georgia Tech)
  • Jennifer Balakrishnan (Boston University)
  • Kirsten Eisenträger (Penn State)
  • David Harbater (University of Pennsylvania)
  • Rachel Pries (Colorado State)
  • Andrew Sutherland (MIT)
  • Sofia Tirabassi (Stockholm University)

An article by the organizers about this topic appears in the February 2019 issue of Notices of the American Mathematical Society: “Thinking Positive: Arithmetic Geometry in Characteristic p”

The deadline for applications has passed.

For questions about the application process, please  contact Kim Kuda at the AMS.

Here is a list of the individuals who participated in this conference:

  • Dean Mitchell Bisogno
  • Jeremy Booher
  • Juliette Bruce
  • Catalina Camacho Navarro
  • William Yun Chen
  • Edgar Costa
  • Huy Dang
  • Soumyadip Das
  • Maria Ines de Frutos Fernandez
  • Ravi Donepudi
  • Ozlem Ejder
  • Ravi K Fernando
  • Maria Fox
  • Sumita Garai
  • Richard Griffon
  • Sachi Hashimoto
  • Katrina Honigs
  • Kelly Isham
  • Jamie Juul
  • Borys Kadets
  • Konstantinos Karagiannis
  • Alicia Mae Lamarche
  • Aaron Landesman
  • Sumin  Leem
  • Wanlin Li
  • Daniel Litt
  • Yuan Liu
  • Nicole Romain Looper
  • Vlad Matei
  • Takumi Murayama
  • Catherine Elizabeth Ray
  • Vinicius Martins Rocha
  • Soumya Sankar
  • Geoffrey Degener Smith
  • Caleb James Springer
  • Emerald T Stacy
  • Libby Taylor
  • Vaidehee Thatte
  • Nicholas George Triantafillou
  • Mckenzie Rachel West
  • + two additional participants