This is the homepage for the 2022 Summer Minicourses, a series of week-long graduate student-run minicourses at UT Austin.

This summer, the minicourses are being organized by Desmond Coles, Amy Li, Saad Slaoui, and Luis Torres. 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

A Gradient Flow Perspective to the Ricci Flow

Instructor: Kenneth DeMason

When and where: July 25–July 29 & August 1–August 5, 11AM–12PM CST. Zoom link available in the Discord channel.

Abstract. This summer mini-course will give brief introductions to concepts in Riemannian Geometry, Gradient flows, and the Ricci flow. The first few days will be devoted to covering essential background in Riemannian Geometry, with the following two days introducing gradient flows and tying them into the 2D Ricci flow. Beginning in the second week we will tackle the higher dimensional Ricci flow, including discussions about singularities, short-time existence of solutions, and its utility. From here we will introduce Perelman's F- and W- functionals to develop the Ricci flow as a type of gradient flow and further characterize singularities.

Introduction to Surface-Knots and Quandles

Instructor: Nicholas Cazet

When and where: July 25–July 29, 3PM–4PM CST. Zoom link available in the Discord channel.

Abstract. I will introduce surface-knot theory and quandle cohomology using the following texts:

  • Surfaces in 4-Space, by Carter, Kamada, and Saito,
  • Surface-Knots in 4-Space, by Kamada, and
  • Quandles and Topological Pairs: Symmetry, Knots, and Cohomology, by Nosaka.
We will start with how to compute the knot group of surface-knots, then discuss foundational results in surface-knot theory. We will conclude with recent results of surface-knots that use the quandle cocycle invariant. Quandles are used to color knots and surface-knots.

    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.