PRIMA 2021 Summer School: Rational curves and moduli spaces in arithmetic geometry

The Pacific Rim Mathematical Association Congress meets in December 2022. A number of summer schools will take place prior to the main event at the end of the year. This summer school is part of the PRIMA Special Session on Arithmetic geometry: theory and computation. In this summer school, we cover two topics:(1) Brauer classes in moduli problems and arithmetic and (2) theory of rational curves and its arithmetic applications.

Brauer classes in moduli problems and arithmetic:

Instructors: Nicolas Addington, University of Oregon and Sarah Frei, Rice University.

We cover Brauer classes, how they arise as obstructions on moduli spaces of sheaves, and how they can be used to obstruct rational points, highlighting recent links between the two.

Course Material 

Morning Worksheet, Aug 2 

Morning Notes, Aug 2 

Course Video: Aug 2, Brauer Classes Lecture 1 

Morning Worksheet, Aug 3 

Morning Notes, Aug 3

Morning Worksheet, Aug 4

Morning Notes, Aug 4 

Course Video: Aug 4: Brauer Classes Lecture 3

Theory of rational curves and its arithmetic applications: 

Instructor: Brian Lehmann, Boston College

We discuss deformation theory of rational curves and Mori’s famous Bend and Break techniques as well as their applications to Geometric Manin’s Conjecture. The lecture series contain introductory components as well as problem sessions and they aim for graduate students and postdocs.

Course Material

Afternoon Exercises, Aug 2

Afternoon Notes, Aug 2

Course Video Aug 2, Rational Curves Lecture 1  

Afternoon Exercises, Aug 3

Afternoon Notes, Aug 3

Course Video Aug 3, Rational Curves Lecture 2 

Afternoon Exercises, Aug 4

Afternoon Notes, Aug 4 

Course Video Aug 4, Rational Curves Lecture 3 

The lecture series contain introductory components as well as problem sessions and they aim for graduate students and postdocs.

Audience:

This summer school is suitable for graduate students and postdoctorates interested in Arithmetic Geometry.

Dates: 

August 2nd - 4th, 2021

Time:

(All times Pacific) 

10:00 — 11:30 Brauer Classes

17:00 - 18:30 Rational Curves

This summer school is a precursor to the Session on Arithmetic Geometry: theory and computation, to be held at the 2022 PRIMA Congress