Mathematics Research Communities, American Mathematical Society

3 690Program ID: MRC-EXPLICIT [#690]
Program Title: Explicit methods in arithmetic geometry in characteristic p June 16-22, 2019
Program Location: Rhode Island, United States [map]
Application Deadline: 2019/02/15 (posted 2018/07/10, updated 2018/06/26, listed until 2019/12/31)
Program Description:    

About the Mathematics Research Communities:

Mathematics Research Communities (MRC), a program of the American Mathematical Society (AMS), nurtures early-career mathematicians--those who are close to finishing their doctorates or have recently finished--and provides them with opportunities to build social and collaborative networks through which they can inspire and sustain each other in their work.

The structured program is designed to engage and guide all participants as they start their careers. For each topic, the program includes a one-week summer conference, a Special Session at the next Joint Mathematics Meetings, and a longitudinal study of early career mathematicians.

Those accepted into this program will receive a flat rate transportation allowance for the summer conference, and will be partially supported for their participation in the Joint Mathematics Meetings which follow in January 2020.

ELIGIBILITY: Individuals within one to two years prior to the receipt of their PhDs, or up to five years after receipt of their PhDs, are welcome to apply.  Most of those supported by NSF funds to participate in the MRC program will be US-based, that is, employed by or a full-time student at a US institution at the time of the MRC summer conference. However, the terms of the grant allow for a limited number of individuals who are not US-based. A few international participants may be accepted. Women and underrepresented minorities are especially encouraged to apply.  All participants are expected to be active in the full MRC program.

For any program, fellowship, prize or award that has a maximum period of eligibility after receipt of the doctoral degree, the selection committee may use discretion in making exceptions to the limit on eligibility for candidates whose careers have been interrupted for reasons such as family or health. Therefore, an applicant who has had to slow down or temporarily stop his or her career for personal reasons may request to be considered for an extension in the amount of time after the PhD degree. Please send exception requests to

  • Completed on-line application form
  • One (1) reference letter submitted by a professor or supervisor who knows the applicant and can address how the applicant will benefit from, and contribute to, the MRC program.

Note that all applicants will be notified of their status by May 1, 2019.

Week 1: June 16 – 22, 2019-- Explicit methods in arithmetic 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.

Application Materials Required:
Submit the following item online at this website to complete your application:
And anything else requested in the program description.

Further Info:
800-321-4267 x 4113
Electronic submission of reference letters is requested.
If this is not possible, contact

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