program Description

The main activity of the Graduate Summer School will be a set of several interwoven minicourses offered by leading experts in the field, designed to introduce students to exciting, current research in mathematics. These minicourses will not duplicate standard courses available elsewhere. Each minicourse comprises three to five lectures. These minicourses vary in level of preparation needed, and the schedule is structured so there are good opportunities for students just entering the field as well as courses suitable for more advanced students. Each course is accompanied by a daily problem session, structured to help students develop facility with the material. Teaching assistants will be available for each minicourse.

Research Topic for 2024: Motivic Homotopy Theory. Motivic homotopy theory arose out of the work of Morel and Voevodsky in the 1990s and since then has developed into both a powerful tool for understanding many arithmetic aspects in algebra and algebraic geometry, as well as being a fascinating generalisation of classical homotopy theory with an active development in its own right. The 2024 GSS on motivic homotopy theory will give participants an introduction to some aspects of motivic homotopy theory as well as a taste of developments in other fields that have been influenced and enabled by motivic homotopy theory. Mini-courses will include: an introduction to unstable motivic homotopy theory, a study of characteristic classes in stable motivic homotopy theory, motivic homotopy theory in enumerative geometry, and a version of Weil conjectures in motivic homotopy theory, as well as courses on recent advances in arithmetic properties of local systems, fundamental problems in Galois cohomology of fields, and aspects of G-bundles in algebraic geometry. Prerequisites: Students should have a basic knowledge of algebraic geometry, algebraic topology, and some homotopy theory. For some of the courses, a knowledge of Galois cohomology and étale cohomology will also be helpful.

APPLICATION PROCEDURE

1. Complete a Standard Coversheet for MathPrograms.Org. Your Standard Coversheet should include the name/s and email address/es of your reference writer/s. One letter of reference is REQUIRED (see below); you may submit up to two references in support of your application.

2. Provide one Reference Letter (REQUIRED). On the application, fill in the checkbox for your reference writer from the name you entered on your Standard Coversheet, then click on the green arrow next to the reference writer’s name so the writer will receive your reference request by email. When notified, your writers will then receive login info and upload instructions to come to the MathPrograms.org site to upload their letters. If your reference writer does not have access to a computer, he or she may submit the reference letter by mail no later than January 15, 2024.

3. Provide your Curriculum Vitae/Resume (REQUIRED): Applicants must upload their CV to their online application.

4. Provide a link to one preprint or publication.(OPTIONAL)