Title: Crepant resolution conjecture for the Hilbert scheme of points on surfaces

Time: Thursday December 22, 2011, 15:00-17:00 pm

Speaker: ProfessorWei-Ping Li (Hong Kong University of Science and Technology)

Title: Crepant resolution conjecture for the Hilbert scheme of points on surfaces

Abstract: The Hilbert scheme of points on a surface is the crepant resolution of the symmetric product of the surface. Ruan Yong-bin formulated a conjecture relating the Chen-Ruan cohomology ring of an orbifold with the cohomology ring of its resolution with quantum corrections by the extremal Gromov-Witten invariants of the resolution. In the joint work with Zhenbo Qin, we proved Ruan's conjecture for the symmetric product of the surface. The method includes vertex algebraic treatment of the cohomology ring of the Hilbert scheme as well as the Chne-Ruan cohomology ring of the symmetric product, co-section localization of Kiem and Jun Li.