This is the homepage for the 2021 Summer Minicourses, a series of week-long graduate student-run minicourses at UT Austin.

This summer, the minicourses are being organized by Arun Debray, Amy Li, Saad Slaoui, and Richard Wong. You can contact us at

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.

This week's courses

Classification of Surfaces

Speakers: Kai Nakamura

Where and When: August 9–13, 2–3PM CDT. Zoom link available in the Slack channel.

Abstract. Surfaces are 2-dimensional manifolds, their classification is fundamental to geometry and topology and to mathematics in general. Our aim will be the topological classification of surfaces, on the way there we will review important topological concepts and tools in this familiar setting of surfaces. A rough outline is as follows:

  1. Basic concepts and background
  2. Triangulations, CW-complexes, and Alg-Top of surfaces
  3. Smooth surfaces, handle decompositions, smooth classifications
  4. Topological surfaces, handle smoothing, and the Kirby torus trick

Integrable systems and quantum groups

Speakers: Surya Raghavendran

Where and When: August 10–14, 2–3PM CDT (Tuesday, Thursday, Friday), 11–12PM CDT (Wednesday), 12–1PM CDT (Saturday). Zoom link available in the Slack channel.

Abstract. The present minicourse will be an introduction to the interplay between solvable models in statistical mechanics and quantum groups. Our guiding examples will be the so-called 6-vertex model and the Heisenberg XXX spin chain; we will find that the solvability of these models is controlled by a quantum group called the Yangian. We'll then discuss some more modern appearances of the Yangian, in a 4d cousin of Chern-Simons theory, and in the geometry of vacua of a class of 2d gauge theories. I hope to make the first three lectures as accessible as possible; other than some philosophical underpinnings, most of the material will only require some linear algebra. The final two lectures will be more prerequisite-intensive, and I will at least assume some familiarity with gauge theory.

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 Slack channel.