# Homotopy Theory Fall 2020

The organizers are Cindy Lester and Ettore Aldrovandi

Planned meeting times are on **Tuesday, 5pm Eastern.** Due to the speakers’ locations, some seminars might be held at the different times to accommodate for the time difference. These times are highlighted below.

The talks are held on Zoom.

- Brandon Doherty, University of Western Ontario
- Tuesday, December 1, 5:00 pm Eastern
*Cubical models of (∞,1)-categories***Abstract:**We describe a new model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical analogue of inner horns. We discuss the proof that this model structure is Quillen equivalent to the Joyal model structure on simplicial sets via the triangulation functor, and a new theory of cones in cubical sets which is used in this proof. We also introduce the homotopy category and mapping spaces of a fibrant cubical set, and characterize weak equivalences between fibrant cubical sets in terms of these concepts. This talk is based on joint work with Chris Kapulkin, Zachery Lindsey, and Christian Sattler, arXiv:2005.04853.

- Nima Rasekh, École Polytechnique Fédérale de Lausanne
- Friday, November 20, 1:25 pm Eastern
*Thom spectra, higher THH and Tensors in ∞-Categories***Abstract:**In this talk we will show how we can use the formalism of presentable ∞-categories and the fact that they are tensored over spaces to present a new and formal method to compute higher THH of various spectra and in particular Thom spectra. This is joint work with Bruno Stonek and Gabriel Valenzuela.

- John Berman, University of Texas, Austin
- Thursday, November 12, 3:35 pm Eastern
**This is the time slot of the Algebra Seminar** *Algebraic K-theory and the zeta function***Abstract:**Deninger suggested that a Weil cohomology theory in Arakelov geometry (not yet constructed) could be used to prove the Riemann Hypothesis. I will survey the relationship between the zeta function and classical cohomology theories. Then I will describe how categorification can be used to construct new cohomology theories in Arakelov geometry, related to algebraic K-theory. I won’t assume any prior knowledge of Arakelov geometry or K-theory.

- Thursday, November 12, 3:35 pm Eastern