## Infinite loop spaces in motivic homotopy theory

### Maria Yakerson (University of Duisburg-Essen (Essen))

Wednesday, March 14, 2018, 15:10 – 16:30

Math -101

Abstract:

Classically in homotopy theory, infinite loop spaces are recognized as spaces with an additional structure: grouplike $E_{\infty}$-spaces. The category of such spaces is equivalent to the category of connective spectra. Replacing topological spaces with smooth schemes, we end up in the realm of motivic homotopy theory, where an analogous statement was sought for since the theory has appeared. In this talk we will discuss the motivic recognition principle, which provides an equivalence between the category of motivic connective spectra and the category of grouplike motivic spaces with so called framed transfers.

This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo.