# Maria Yakerson: The space of algebraic cobordism

**Time: **
Wed 2019-01-23 11.00 - 12.00

**Lecturer: **
Maria Yakerson (Essen)

**Location: ** Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

Abstract: Classically, the universal oriented cohomology theory is represented by the complex cobordism spectrum MU, which has a description in terms of cobordism spaces of compact smooth manifolds with an extra structure. In motivic settings, the analogous spectrum MGL was constructed by Voevodsky, and over a base field of characteristic 0, its corresponding homotopy groups can be expressed via algebraic “cobordism groups” of varieties, as defined by Levine-Morel. In this talk we will discuss a model for the underlying space of MGL as an algebro-geometric incarnation of the cobordism space. As an application, we will present a geometric description of this space as a (homotopy type of) some Hilbert scheme. This is joint work with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo.