Characteristic Classes in Stable Motivic Homotopy Theory - Part 4

Explore the fourth lecture in a series on characteristic classes in stable motivic homotopy theory, delivered by Frédéric Déglise from CNRS and ENS Lyon. Delve into advanced mathematical concepts that bridge differential geometry with stable motivic homotopy theory, examining how varieties and CW-complexes translate to algebraic varieties and schemes. Learn about the extension of Quillen's work by Levine and Morel, and discover emerging topics in Panin and Walter's orientation theories leading to quadratic enumerative geometry. Part of the 2024 Graduate Summer School program at PCMI, this lecture builds upon fundamental knowledge of algebraic geometry, algebraic topology, and homotopy theory, with additional insights enhanced by understanding of Galois cohomology and étale cohomology. Access complementary lecture notes and problem sets to reinforce understanding of these advanced mathematical concepts within the broader context of motivic homotopy theory's applications in algebra and algebraic geometry.