EVENT DETAILS AND ABSTRACT

Title: Hodge theory in non-commutative algebraic geometry
Speaker: Dmitry Kaledin
Speaker Info: Steklov Mathematics Institute and Independent University of Moscow
Brief Description:
Special Note:
Abstract:

Hodge theory is of course an invaluable tool in algebraic geometry. "Non-commutative algebraic geometry", or "geometry of derived categories", is a recent development which appeared out of an empirical observation: surprisingly many invariants an algebraic variety X is known to possess depend only on the derived category D^b(X) of coherent sheaves on X, and make sense for much more general triangulated categories. I will try to illustrate this observation, with Hodge theory being the case in point. I will also try to show that for some questions, it is the non-commutative point of view which is actually more natural. If time permits, I will also explain how this fits together with recent work on "semi-topological K-theory" by Friedlander and Walker, and its non-commutative rephasing by Toen.