Adeel Khan: Motivic infinite loop spaces
Time: Tue 2018-10-09 13.15 - 15.00
Location: Room 34, House 5, Kräftriket, Department of Mathematics, Stockholm University
Participating: Adeel Khan (University of Regensburg)
ABSTRACT: Given a homotopy type X, May’s recognition principle says that a structure of infinite loop space on X is equivalent to a grouplike \(E_\infty\)-monoid structure. I will discuss an analogue of the theory of \(E_\infty\)-spaces in the setting of motivic homotopy theory, and two applications. The first is a recognition principle for motivic infinite loop spaces (over any perfect field). The second is a representability result for the motivic sphere spectrum, in terms of a “framed" version of the Hilbert scheme of points in affine space. This is joint work with E. Elmanto, M. Hoyois, V. Sosnilo and M. Yakerson.