This is the homepage for the 2024 Summer Minicourses, a series of week-long graduate student-run minicourses at UT Austin.

This summer, the minicourses are being organized by Jacob Gaiter and Luis Torres. You can contact us at SMC.Organizers@gmail.com.

What are summer minicourses?

Minicourses focus on tools, methods, and ideas that aren't usually covered in prelims but are useful in topics classes/research. The idea is that a week-long minicourse will remain engaging, be easier to schedule, and help provide focus. These courses are primarily for graduate students, but all are welcome to participate!

Past courses have included:

  • Review of classes that were taught in previous years.
  • Primers for classes that will be taught next year.
  • Examples of useful computational tools.
  • Introductions to a subject/research area.

The 2024 Summer Minicourses have been scheduled!

Please check the schedule for updated abstracts and minicourse times. Meeting links for the minicourses will be sent to the mailing list and/or on the appropriate Discord Channel

If you are interested in participating in a minicourse, click here to join the SMC Discord.

The next course:

Cartan Geometry

Instructor: Toby Aldape

When and where: July 8–July 12, Time TBA. Zoom: TBA

Abstract. Cartan geometry is an extremely general framework, based on differential geometry, that encompasses Riemannian, conformal and projective geometries and many others. We will start by quickly introducing Lie groups, Lie algebras, the Lie group-Lie algebra correspondence, principal bundles, and differential forms. Next I’ll talk about Klein pairs, which formalize the notion of a geometry, and give several examples. After that we’ll cover the Maurer-Cartan form of a Lie group, its generalization by the principal bundle definition of Cartan geometry, and the concept of curvature in this context. The example of Riemannian geometry will provide motivation for this definition. Finally, we’ll introduce mutation, which allows us to translate between closely related geometries, like the geometries based on flat, elliptic, and hyperbolic space.


These courses were inspired in large part by the ones held at University of Michigan, which were started by Takumi Murayama.

You can click here to be added to the email list and click here to join the Discord server.