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This is the webpage for the Graduate Student Homotopy Theory Seminar (GSHTS) at UIUC.
Location and Time
For the Spring 2026 semester, we meet Monday 4-5pm in room 156 of Henry Administration Building.
Talk Schedule
| Day | Speaker | Title and Abstract |
|---|---|---|
| 02/23/2026 |
Doron Leonardo Grossman-Naples |
Spectral Deformation Theory and the Hilbert Stack The question of representability for moduli problems is a central one in algebraic geometry, and spectral algebraic geometry is no exception to this. The most significant tool we have in this regard is what I call the "spectral deformation of representability". This theory, developed by Jacob Lurie, allows us to use deformation theory to reduce spectral moduli problems to their classical analogues. I will give a general overview of the theory, then describe an application from my own research: the representability of the Hilbert functor of a spectral algebraic space. |
| 03/02/2026 |
Timmy Feng |
Stefanich Rings: Delooping of the Multiplication The duality between an algebraic variety and its ring of regular functions is a cornerstone of algebraic geometry. To recover an algebraic stack with affine diagonal, however, one must pass one categorical level higher and consider its derived category of quasi-coherent sheaves. In general, Tannakian formalism has its limit - even derived categories fail to distinguish different stacks. In this talk, we will explain how richer layers of information can be encoded by successively passing to higher categorical structures. We will also introduce Stefanich rings, which may be viewed as commutative rings equipped with infinite deloopings of the multiplication. We will follow the notes Geometry and Higher Category Theory by Scholze. |
| 03/09/2026 |
| |
| 03/23/2026 |
Langwen Hui |
Stefanich Rings: Examples and Applications This talk will continue our discussion of Stefanich rings. We will review their basic properties and present several examples. Time permitting, we will also explain their relationship with six-functor formalisms and applications to a general form of Cartier duality. |
| 03/30/2026 |
Jiantong Liu |
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| 04/06/2026 |
Vivasvat |
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| 04/13/2026 |
Levi | |
| 04/20/2026 |
Haoran | |
| 04/27/2026 |
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| 05/04/2026 |
Talks from previous semesters may be found in the archive.