# Algebra/Topology Seminar

Speaker: Marc Hoyois

Title: Towards higher algebraic cobordism.

Abstract: Voevodsky introduced the algebraic cobordism spectrum MGL in his proof of the Milnor conjecture. Later, Levine and Morel defined the algebraic cobordism group Ω(X) of an algebraic variety X by explicit generators and relations. In characteristic zero, it is now known that Ω(X) is the zeroth MGL-cohomology group of X, but there is still no geometric understanding of the higher algebraic cobordism groups. In joint work with E. Elmanto, A. Khan, V. Sosnilo, and M. Yakerson, we prove that the higher algebraic cobordism groups are, in some range, the homotopy groups of certain spaces whose points are algebraic varieties and whose paths are cobordisms between them.