Decompositions of varieties, birationality, and K theory (Inna Zakharevich)

In this talk we investigate the higher homotopical structure that can be added to the Grothendieck ring of varieties using algebraic K-theory. Using the tools of homotopy theory, we analyze this new structure to learn about how the dimension filtration on the Grothendieck ring behaves, and how it interacts with the birational automorphism groups.