|Speaker:||Wai-Kit Yeung (Kavli IPMU)|
|Date:||Tue, Nov 24, 2020, 15:30 - 17:00|
A Calabi-Yau category (after Ginzburg, Kontsevich-Vlassopoulos, Brav-Dyckerhoff) is a category with a self-dual structure that generalizes both Serre duality and Poincare duality. In a certain natural sense, this self-dual structure can be viewed as a noncommutative analogue of a
symplectic structure. Using a similar analogy, one can develop a noncommutative analogue of a Poisson structure. Such a notion is called a pre-Calabi-Yau category, first studied by Kontsevich and Vlassopoulos. Natural examples of such arise in algebraic geometry, topology, symplectic topology, etc.
In this talk, we give an introduction to several aspects of this notion.