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This is the webpage for the Graduate Student Homotopy Theory Seminar (GSHTS) at UIUC.
Location and Time
For the Fall 2025 semester, we meet Friday 3-4pm in room 141 of Altgeld Hall.
Talk Schedule
| Day | Speaker | Title and Abstract |
|---|---|---|
| 09/12/25 |
Timmy Feng |
Loop spaces in derived algebraic geometry I will introduce various loop spaces, including rational, trigonometric, and elliptic loop spaces, and discuss their degenerations. I will explain how the HKR filtration can be derived from deformation to the normal cone. If we have time, I will also discuss the lift to the sphere spectrum, which leads to a filtration of topological Hochschild homology. |
| 09/19/25 |
Doron Leonardo Grossman-Naples |
Isogenies of Oriented Elliptic Curves In the classical setting, isogenies (particularly in the form of level structures) are a crucial tool for studying modular forms and elliptic curves. But how do they behave for the higher-algebraic version of this story, elliptic cohomology? Ramified isogenies make this question difficult. In this talk, I will describe my proof that the moduli of isogenies of oriented elliptic curves is in fact a formal (nonconnective) spectral Deligne-Mumford stack. Along the way, we'll encounter the moduli of isogenies of the Quillen formal group, some deformation theory computations made possible by a beautifully simple trick, and (time permitting) an application to level structures. |
| 09/26/25 |
Yigal Kamel |
The Anderson—Brown—Peterson splitting of spin bordism In the 1960s, Anderson, Brown, and Peterson (ABP) introduced KO-valued characteristic classes in order to study SU bordism and the Kervaire invariant. Shortly after, they showed that on spin manifolds, each KO-characteristic class has a particular filtration level, which led to a 2-local splitting of the spectrum MSpin. As a corollary, they characterize when two spin manifolds are spin cobordant by identifying a sufficient set of characteristic numbers. In this talk, I will discuss ABP’s construction and some applications. Time permitting, I will discuss parts of the proof, as well as joint work with Hassan Abdallah incorporating Reality into the ABP splitting. |
| 10/03/25 |
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| 10/10/25 |
Juhan Kim |
The Delooping of F1-modules While F1-geometry is still at developing stage, it has seen many meaningful progresses so far, including attempts of giving a framework of doing homotopy theory in F1 sense. In this talk, I'll briefly explain Beardsley's idea of applying the bar construction in the context of F1-modules and related results. |
| 10/17/25 |
Ea E Thompson |
Exponentiable Virtual Double Categories and Representability Virtual double categories have been shown to provide an effective framework for formal category theory, from characterizations of adjoints and liftings to descriptions of pointwise Kan extensions and Yoneda structures. In studying virtual double categories themselves, an interesting question comes from asking what kind of structure virtual double categories are enriched over. In this talk, we take a first step in answering this question by providing a number of equivalent descriptions of the exponentiable virtual double categories. We will provide examples of exponentiable virtual double categories, including pseudo double categories and cospan virtual double categories, while also providing a simple counter-example to the claim that all virtual double categories are exponentiable. If there is time, we will discuss sufficient conditions for exponentials to be represented by pseudo-double categories, as well as connections to the characterization of exponentiable multicategories. |
| 10/24/25 |
Langwen | |
| 10/31/25 |
Jiantong | |
| 11/07/25 |
Jesse | |
| 11/14/25 |
Levi | |
| 11/21/25 |
Vivasvat | |
| 12/05/25 |
Fredrick |
Talks from previous semesters may be found in the archive.