PIMS Algebraic Geometry Seminar

Speakers:

(1) Zheng Hua, University of Hong Kong (2:30-3:30)

Title: Noncommutative differential calculus and Calabi-Yau geometry

Quivers with potential appear naturally in the study of the deformation theory of objects in 3D Calabi-Yau categories, for example the deformation of vector bundles on 3D Calabi-Yau manifolds. They provide a deep link between geometry of Calabi-Yau manifolds to some aspects of representation theory, for example cluster algebras, quantum enveloping algebras, etc. In this talk, I will survey some recent progress in non commutative differential calculus of quivers with potentials, and show how this leads to new results in birational geometry and Donaldson-Thomas theory.

(2) Angelo Vistoli, Scuola Normale Superiore (4:00-5:00)

Title: The Chow ring of the stack of stable curves of genus 2

There is now an extensive theory of rational Chow rings of moduli spaces of smooth curves. The integral version of these Chow rings is not as well understood. I will survey what is known. In the last part of the talk I will discuss the Chow ring of the stack of stable curves of genus 2, which has been recently calculated by Eric Larson. I will present a different approach to the calculation, which offers an interesting point of view on stack of stable curves of genus 2. This part is joint work with Andrea Di Lorenzo.

This series is part of the PIMS CRG on Geometric Algebra.