Home
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 |
||
| 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 | |
| 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.