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 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.


This week's courses


Perverse Sheaves

Speakers: Mark Macerato

Where and When: July 19–23, 1:00–2:30PM CDT. Zoom link available in the Slack channel.

Abstract. This course will give a (topologically motivated) introduction to perverse sheaves and intersection (co)homology. The first lecture will introduce intersection homology (following Goresky and MacPherson) and review classical results on the topology of complex algebraic varieties. From there, we will discuss the relevant background in homological algebra (derived categories and derived functors) and the constructible derived category of sheaves in order to formulate intersection homology sheaf theoretically. In the third lecture, we will introduce and prove Verdier duality and consequently Poincare duality for singular spaces. The fourth lecture will finally define the perverse t-structure and establish the basic properties of perverse sheaves on complex varieties. To illustrate the general theory, we will study perverse sheaves on curves. Finally, in the last lecture, we will state the decomposition theorem, discuss its proof, and give some applications in algebraic geometry or representation theory (depending on the audience's taste). The presentation will be relatively elementary, but will assume a general familiarity with algebraic topology, algebraic geometry, and classical homological algebra.



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.