RTG Research Workshop

This is the website for the Spring 2021 research workshop associated with the Berkeley RTG Number Theory and Arithmetic Geometry.

The purpose of the workshop is to bring together students and faculty for a week of focused activity to learn about new developments and research areas. The workshop will have lecture series in the mornings and discussion/problem solving sessions in the afternoons.

Dates: June 14-18, 2021

Lecture Series

Jennifer Balakrishnan (Boston University):

Title: Chabauty--Coleman and Chabauty--Kim experiments

Abstract: We will explore the computation of rational points on curves via Chabauty--Coleman and Chabauty--Kim sets. We will study the extra points that may arise in these sets, in view of a conjecture of Kim. Throughout, we will present a number of examples, in the case of curves of genus 2 and 3 (in work of Bianchi, as well as in joint work with Dogra, and joint work with Bianchi, Cantoral-Farfán, Çiperiani and Etropolski).

Jordan Ellenberg (University of Wisconsin) and David Zureick-Brown (Emory University):

Title: Rational points: what's new, what's next.

Abstract: The study of rational points on varieties over global fields — that is, the subject of Diophantine geometry — is one of the oldest parts of number theory. Yet we still know almost nothing about it. This has not stopped people from striking out in new directions and asking new questions. That’s just how we are. Ellenberg and Zureick-Brown will outline the basics of which varieties have a lot of rational points and which not so many, and then discuss more refined questions of contemporary research interests, which might touch on: Batyrev-Manin heuristics, arithmetic statistics, heights on stacks, Peyre’s notion of “free rational points,” rational points and rational curves, recent work on the shape of number fields, etc. We will try to keep the focus on the existence of a lot of interesting questions that remain unanswered and even more that remain unasked.

Location:

All lectures will be via Zoom. Meeting ID etc. will be provided to registered participants closer to the event.

Registration:

All participants are asked to register. The registration form can be accessed here.

Schedule:

All times are Pacific Daylight Time, and lectures will start at the indicated times (so not following the practice of "Berkeley time").

Lectures:

Monday June 14:

10-11: Ellenberg/Zureick-Brown

11:15-12:15: Balakrishnan, Notes

Tuesday June 15:

11-12: Balakrishnan, Notes

1-2: Ellenberg/Zureick-Brown

Wednesday June 16:

10-11: Ellenberg/Zureick-Brown

11:15-12:15 Balakrishnan, Notes

Thursday June 17:

10-11: Balakrishnan, Notes

11:15-12:15 Ellenberg/Zureick-Brown

Friday June 18:

10-11:30 Working group presentations

Working Sessions:

The working sessions will be held in their own separate Zoom rooms; meeting information will be shared by email and at the first lecture.

Balakrishnan: 2:10-3pm Mon-Thurs

Ellenberg/Zureick-Brown: 3:10-4pm Mon-Thurs