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This is the webpage for the Graduate Student Homotopy Theory Seminar (GSHTS) at UIUC.

Location and Time

For the Spring 2025 semester, we meet Mondays 1-2pm in room 143 of Altgeld Hall.

Talk Schedule

Day	Speaker	Title and Abstract
02/10/25	Langwen Hui	Computing homotopy groups of tmf Topological modular forms (tmf) is a spectrum that interacts in interesting ways with geometry and arithmetic. In this talk I will examine this object from the angle of stable homotopy theory, and sketch a computation of its homotopy groups, which is a blend of classical modular forms and the stable homotopy groups of spheres.
02/24/25	Samuel Hsu	Opetopic types in homotopy type theory Homotopy type theorists have celebrated some major successes in formalizing (and often generalizing) results from classical homotopy theory. For many results from modern homotopy theory however, we must confront the issue of defining ∞-categories inside HoTT. Very roughly, the problem is that HoTT is designed to internalize the infinite coherences of only a very particular class of higher structure, namely (globular) ∞-groupoids, and not any other higher structures. This issue has plagued HoTT since the very start. By now there are several proposed approaches, each adding on top of HoTT with various advantages and drawbacks. In this talk we will give an overview of the solution put forth by Finster, Allioux, and Sozeau using opetopic types. Some familiarity with type theory will be helpful, although the emphasis will be such that prerequisites can be kept to a minimum, and we will quickly review some at the start. Note: this talk will be on zoom.
03/03/25	Doron Grossman-Naples	Computing Pullbacks of ∞-Topoi; or, How I Learned to Stop Worrying and Love Gabriel-Ulmer Duality Fiber products are a pretty fundamental construction in geometry, so it's not surprising that pullbacks of ∞-topoi arise quite naturally when studying spectral algebraic geometry. Fortunately, Lurie has shown that the category of ∞-topoi has all (small) limits. Actually computing them is another matter, however, as I discovered when doing so became necessary for my research. There isn't quite a complete recipe, and even the constructive aspects depend on some surprisingly abstract categorical machinery. Join me in this talk as I walk you through this journey: why you might want to undertake it, the category-theoretic structure that makes it possible, and what such a computation actually looks like.
03/24/25	Johnson Tan	TBD TBD
03/31/25	Timmy Feng	TBD TBD
04/07/25	Ea E	TBD TBD
04/14/25	Jiantong Liu	TBD TBD
04/21/25	Levi Poon	TBD TBD
04/28/25	Yigal Kamel	TBD TBD
05/05/25	Juhan Kim	TBD TBD

Talks from previous semesters may be found in the archive.