This page contains the schedule for the Summer 2023 mathematics graduate student-run minicourses at UT Austin. Note that all times are in Central Daylight Time (UTC -5). Minicourses will be run using one of three lecture formats:

  • "In-person" lectures will be held in-person at UT Austin in PMA 9.166 without a Zoom option.
  • "Zoom" lectures will be held over Zoom without an in-person option.
  • "Hybrid" lectures will feature both an in-person and Zoom option.
Though not all course abstracts and times have been determined yet, they will be posted here before each course's start date but may change over time. Individual Zoom links will be made available closer to their respective course start dates.

Topic Speaker(s) Dates Time (CDT) Format Abstract
Hilbert's 19th problem Jeffrey Chang June 6–June 16 10am–12pm Hybrid

Abstract. A complete solution to Hilbert's 19th problem will be presented. This will include the Euler-Lagrange equations, the Schauder theory, and the De giorgi theory.
Introduction to Teichmüller Dynamics Hunter Vallejos July 17–July 21 1pm–2pm Zoom

Abstract. The goal of the course is outline some of the basic objects involved in Teichmüller dynamics (such as Teichmüller space, quadratic differentials, measured laminations, etc.), followed by a presentation of a few big results in the field.

Possible topics to be covered include Siegel-Veech constants and the Siegel-Veech formula, the shape of random translation surfaces, ergodic and mixing properties of Teichmüller geodesic flow, Thurston's stretch maps and earthquake flow, and Mirzakhani's conjugacy. (This list is way too ambitious and we'll probably only do a couple of these).

A Geometric Proof of Rokhlin’s Theorem William Winston June 26–June 30 1pm–2pm Zoom

Abstract. Rokhlin’s theorem is one of the earliest classification theorems of smooth 4-manifolds. In this minicourse, I will describe a geometric proof of Rokhlin’s theorem from Kirby’s book, which is based on a paper by Freedman and Kirby. Some aspects of the proof include spin structures and bordism on low-dimensional manifolds; working with the intersection form of a 4-manifold; and handle moves. This minicourse assumes familiarity with standard algebraic and differential topology. We will emphasize examples and computations which I hope will be helpful for further topics on 4-manifolds.

Symplectic Cohomology Jacob Gaiter June 19–June 23 9am–10am Zoom

Abstract. This is an algebraic gadget which one can use to study a Liouville domain (A particular kind of exact symplectic manifold with boundary) which plays an important roll in homological mirror symmetry.