Speaker: Sergey Galkin

Title: Calculus of algebraic dynamics

Date: June 26, 2015, 11:00-12:00

Place: 2nd SwissMAP Geometry and Topology conference, Les Diablerets

First I recall how one can do calculus of algebraic geometry with values in Grothendieck's ring of varieties, with examples of formulas, and relation to birational geometry. Then I explain what are the higher K-theory counterparts to Grothendieck's ring of varieties what is the explicit description of K_1(Vars), and what could be a calculus of automorphisms there. Finally, I explain a tentative construction of the Hochschild homology counterpart, HH(Vars). I hope one should be able to do calculus of endomorphisms in this group, and I will explain how to twist Chern characters of known formulas in K_0(Vars) by endomorphisms. Definition of higher K_i(Vars) and an explicit construction of K_1(Vars) was explained to me by Evgeny Shinder three years ago. It was independently found by Inna Zakharevich about the same time, and it appears in her recent preprints 1506.06197, 1506.06200.