Title: Introduction to noncommutative algebraic geometry

Speaker: Zijing Ye

Abstract: I will introduce some of Michel Van den Bergh's work on noncommutative resolutions. In short, the theory is to show that the derived category of a resolution of a singular variety is isomorphic to a derived category of a noncommutative algebra, known as the noncommutative resolution. I will explain how to construct the tilting bundle that provides this noncommutative resolution. To illustrate, I will explicitly calculate the Atiyah flop example.