EVENT DETAILS AND ABSTRACT

Title: The universal property of the multiplicative structure of Thom spectra
Speaker: Omar Antolin Camarena
Speaker Info: Harvard
Brief Description:
Special Note:
Abstract:

The theory of Thom spectra associated to stable spherical fibrations has been developed by many authors including Mahowald, Lewis, May, Quinn, Ray and Sigurdsson. A stable spherical fibration is classified by a map X → BGL₁(S) and Lewis showed that if this map is an infinite loop map or an n-fold loop map then the Thom spectrum is an E_∞- or E_n-ring spectrum, respectively. Ando, Blumberg, Hopkins, Gepner and Rezk introduced a new approach to Thom spectra using the language of ∞-categories. Using their approach, we will explain how to apply some simple (∞-)category theory to study multiplicative structures on Thom spectra, proving a generalization of Lewis's theorem and moreover characterizing the ring structure by a universal property. We will also describe some applications of this characterization which are work in progress with Tobias Barthel.