Noncommutative algebraic varieties, their properties and geometric realizations II

Homological Mirror Symmetry (minicourse)
Topic:Noncommutative algebraic varieties, their properties and geometric realizations II
Speaker:Dmitry Orlov
Affiliation:Steklov Mathematical Institute, Russian Academy of Sciences; Member, School of Mathematics
Date:Wednesday, February 8
Time/Room:10:45am - 12:00pm/S-101
Video Link:https://video.ias.edu/homological/2017/0208-DmitryOrlov

Continuation of Friday, Feb 3 minicourse. We will discuss a notion of noncommutative and derived algebraic variety. This approach comes from a generalization of derived categories (quasi) coherent sheaves on usual algebraic varieties and their enhancements. We are going to talk about different properties of noncummutative varieties such as regularity, smoothness and properness. A new operation of gluing of noncommutative varieties will be introduced. We also will define a some notion of geometric realization of noncommutative varieties, and will give explicit examples of such realizations, in the case of special exceptional collections.