By Omar Antolín (Universidad Nacional Autónoma de México).

I will describe the ∞-categorical approach developed by Ando, Blumberg, Gepner, Hopkins, and Rezk to Thom spectra of stable spherical fibrations. I will also mention joint work with Tobias Barthel that uses this approach to study the multiplicative structure of such spectra. This multiplicative structure is characterized by a universal property, which is more useful than might seem given its simplicity. As an application we will discuss E_n-orientations and the Thom isomorphism.

I won't assume familiarity with either ∞-categories or with E_n-ring spectra; on the contrary, I hope this mini course will serve as an introduction to these topics.