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Summer Graduate School

Geometry and Dynamics in Higher Rank Lie Groups (St. Mary's College) July 14, 2025 - July 25, 2025
Parent Program:
Location: St. Mary's College
Organizers Richard Canary (University of Michigan), Sara Maloni (University of Virginia), Wenyu Pan (University of Toronto), Cagri Sert (University of Zurich), LEAD Tengren Zhang (National University of Singapore)

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<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. 


The following are the prerequisites for the summer school.

  • Basic group theory. This includes notions such as finitely generated groups, continuous actions of topological groups, and proper discontinuity.
  • Basic covering space theory. This includes notions such as the fundamental group, covering spaces, deck groups, and the universal cover.
  • Basic measure theory. This includes notions such as pushforward measures, product measures, absolute continuity, Radon-Nikodym derivatives, and weak convergence of measures.
  • Basic principles of Riemannian manifolds. This include notions such as smooth and analytic manifolds, vector bundles, vector fields, and metrics and norms on vector bundles.

Application Procedure

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

Keywords and Mathematics Subject Classification (MSC)
  • Lie groups

  • discrete groups

  • geometric structures

  • Teichmuller theory

  • entropy

  • ergodicity

  • mixing

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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