Summer Graduate School

<p>Flats and hyperbolic planes in a higher rank symmetric space</p> Drawn by Steve Trettel.

Lie groups are central objects in modern mathematics; they arise as the automorphism groups of many homogeneous spaces, such as flag manifolds and Riemannian symmetric spaces. Often, one can construct manifolds locally modelled on these homogeneous spaces by taking quotients of their subsets by discrete subgroups of their automorphism groups. Studying such discrete subgroups of Lie groups is an active and growing area of mathematical research. The objective of this summer school is to introduce young researchers to a class of discrete subgroups of Lie groups, called Anosov subgroups. These subgroups are central objects in the study of higher Teichmuller theory, convex projective geometry, and character varieties. In this summer school, there will be an emphasis on discussing some of the dynamical tools that have recently been successfully used to study Anosov subgroups. The required background in dynamics, hyperbolic geometry, and Lie theory will also be discussed. Aside from providing a stimulating academic environment for learning about Anosov subgroups, this summer school also aims to be a relaxed and friendly space for participants to interact with fellow aspiring mathematicians. There will also be many opportunities for participants to consult with the expert lecturers of the summer school. Join us for an unforgettable fortnight of discovery and learning!

School Structure

There will be two lectures each day, as well as two problem sessions. 

Google drive for uploading problem sets: https://drive.google.com/drive/folders/1oPbB4KQKEK0BxNPEM0_zxsL1B9gNWp9W

Prerequisites

The following are the suggested prerequisites for the summer school.

(1) Algebra prerequisites

• Groups and group actions: Part I of Abstract Algebra by David S. Dummit and Richard M. Foote
• Linear algebra: Part III of Abstract Algebra by David S. Dummit and Richard M. Foote

(2) Topology prerequisites 

• Point set topology: Chapters 1–7 of Topology by James Munkres
• Covering spaces: Chapter 1 of Algebraic Topology by Allen Hatcher; Chapters 9–12 of Topology by James Munkres
• Differential topology and Riemannian geometry: Chapters 1–14 of Introduction to Smooth Manifolds by John M. Lee (errata)

(3) Lie groups prerequisites

• Chapters 1–8 of Lie Groups, Lie Algebras, and Representations by Brian C. Hall

(4) Analysis prerequisites

• Measure theory: Chapters 11–15 of Real Analysis by H.L. Royden

Application Procedure

For eligibility and how to apply, see the Summer Graduate Schools homepage.