Colloquium: Alexander Efimov (HSE)

Alexander Efimove gives a talk titled "Categorical Noncommutative Geometry" as part of the Math Department's colloquium series.
Abstract:
I will give a brief overview of the categorical approach to algebraic geometry. The idea is to study algebraic varieties (or schemes) via their derived categories of coherent sheaves, considered as differential graded (dg) categories. One can consider more general dg categories (with some finiteness conditions) as noncommutative algebraic varieties (or schemes).
It turns out that the notions of smoothness and properness make sense in this context, as well as classical invariants such as de Rham cohomology and K-theory. I will give an overview of some results in this field.