## EVENT DETAILS AND ABSTRACT

**Colloquium**
**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.

**Date:** Wednesday, February 10, 2010

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Ezra Getzler

**Contact email:** getzler@northwestern.edu

**Contact Phone:**

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