Marc Hoyois (Northwestern University): Quillen's theorem for algebraic cobordism.

Algebraic cobordism MGL was introduced by Voevodsky as an algebro-geometric analogue of complex cobordism MU: it is the universal oriented cohomology theory for smooth schemes. A fundamental result in homotopy theory is Quillen's identification of the homotopy groups of MU with the Lazard ring. Voevodsky conjectured an analogous result for MGL, and his conjecture was recently proved for regular schemes of characteristic zero and up to p-torsion for regular schemes of charateristic p>0. I will explain Voevodsky's conjecture and sketch the proof in these cases.