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:
For two days each, three visiting advisors will be on site:
Also, throughout the week via Skype, external advisors will be available for participant consultations:
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.