Characteristic Classes in Stable Motivic Homotopy Theory - Part 3

Explore the third lecture in a series on characteristic classes in stable motivic homotopy theory, delivered by Frédéric Déglise from CNRS and ENS Lyon. Delve into the extension of classical differential geometry concepts to algebraic varieties and schemes, building upon Voevodsky's proof of the Milnor conjecture. Learn how Quillen's work on formal group laws and cobordism has been successfully adapted by Levine and Morel in the motivic context, and discover emerging developments in orientation theories by Panin and Walter that lead to quadratic enumerative geometry. Part of the 2024 Graduate Summer School program at PCMI, this advanced mathematics lecture requires foundational knowledge in algebraic geometry, algebraic topology, and homotopy theory, with additional background in Galois and étale cohomology being beneficial. Access comprehensive lecture notes and problem sets to reinforce understanding of this sophisticated mathematical framework that bridges differential geometry and stable motivic homotopy theory.