Summer Mini-Courses 2025

This is the homepage for the 2025 Summer Minicourses, a series of week-long graduate student-run minicourses at UT Austin.

This summer, the minicourses are being organized by Toby Aldape, Jacob Gaiter, Luis Torres, and Ryan Wandsnider. 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.

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.

This week's courses:

Machine Learning for Data Science

Instructor: Addie Duncan

When and where: July 7 - July 11 and July 14 - July 18, Times: 6PM-7PM. Zoom

Abstract. Data Science is the study of extracting meaningful insights from data. It combines a variety of disciplines including mathematics, statistics, and computer science. Data science is a rich field and covers a variety of tasks including data storage and management, data engineering, machine learning, data visualization, and more. In this course we will focus on using Machine learning to make predictions or uncover patterns in data that can be translated into real world ideas. Machine learning itself is also vast and rich field so we will focus mainly on supervised and unsupervised machine learning algorithms and how they can be applied to tabular data. Though during our study, we may discuss ways that machine learning can be used to process text and images. The purpose of the course is 2-fold. We will spend the first half learning a general overview of the mathematics behind popular machine learning algorithms and data processing techniques. In the second part we will work in groups to implement what we’ve learned to analyze a data set.

Next Week's Courses:

Computing Sheaves in Representation Theory

Instructor: JiWoong Park

When and where: July 21-25, Times: 11AM-12PM and 2PM-3PM, Hybrid, PMA 9.166, Zoom

Abstract.

Abstract. Sheaf categories on spaces such as the flag variety and affine Grassmannian encode rich representation-theoretic structures, making sheaf theory an essential tool in the study of geometric representation theory. This minicourse will focus on explicit computations involving sheaves, each situated in important contexts such as the Kazhdan–Lusztig conjecture, the geometric Satake equivalence, and Soergel’s conjecture. The course has two main objectives:

1.To make the abstract formalism of sheaf theory more approachable by working through concrete, computation-based examples.

2.To provide exposure to foundational results in geometric representation theory by situating each computation within its relevant representation-theoretic context.

Although several types of sheaves arise in representation-theoretic applications, this course will focus exclusively on constructible and perverse sheaves.

Spin Geometry

Instructor: Adrian Flores

When and where: July 21 - July 25, Times: 1PM-2PM, PMA 11.166

Abstract. Going to try and cover the relevant topics in the first two chapters of "Spin Geometry" by Lawson and Michelsohn with examples as they relate to Seiberg-Witten theory.

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