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

Abstract:

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.