Fall 2024 Algebraic topology seminar
Where:
507 Mathematics
When:
Fridays 11am-12pm
| Date | Speaker (affiliation) | Title & Abstract |
| October 11 (This talk will be in Mathematics 203) | Myungsin Cho (Indiana University Bloomington) | Fiber of the cyclotomic trace of the sphere spectrum and K-theoretic Tate-Poitou duality at the prime 2Abstract: Understanding the algebraic K-theory of the sphere spectrum has long been recognized as a fundamental problem in algebraic and differential topology. Since the homotopy fiber of its p-completed cyclotomic trace depends only on the zeroth homotopy group, we can apply algebraic methods to study it. Blumberg and Mandell’s work demonstrates that, for odd primes, Tate-Poitou duality can be enhanced to an Anderson duality between the homotopy fiber and the K(1)-local K-theory of the integers. In this talk, I will present this connection and extend the result to the case where p=2. |
| October 18 | Candace Bethea (Duke University) | The local equivariant degree and counting rational curves equivariantlyAbstract: I will talk about joint work with Kirsten Wickelgren on defining a global and local degree in stable equivariant homotopy theory. We construct the degree of a proper $G$-map between smooth $G$-manifolds and show a local to global property holds. This allows one to use the degree to compute topological invariants, such as the equivariant Euler characteristic and Euler number. I will discuss the construction of the equivariant degree and local degree, and I will give an application to counting orbits of rational plane cubics through 8 general points invariant under a finite group action on $\mathbb{C}\mathrm{P}^2$. This gives the first equivariantly enriched rational curve count, valued in the representation ring and Burnside ring. This equivariantly enriched count also recovers a Welchinger invariant in the case when $\mathbb{Z}/2$ acts on $\mathbb{C}\mathrm{P}^2$ by conjugation. |
| October 25 | Rachael Boyd (University of Glasgow) | TitleAbstract: |
| November 1 | Viktor Burghardt (University of Michigan) | TitleAbstract: |
| November 8 | Natalie Stewart (Harvard University) | TitleAbstract: |
| November 15 | Andres Mejia (University of Pennsylvania) | TitleAbstract: |
| November 22 | Roy Magen (Columbia University) | TitleAbstract: |
| December 6 | Marco Volpe (University of Toronto) | TitleAbstract: |