Intersection theory and tautological rings of moduli spaces of curves

Thursday, January 17, 2013 - 15:00 to 15:50
Speaker Information
Hao Xu
Harvard University

Notes

Recruitment talk

Abstract or Additional Information

Mumford initiated a systematic study of intersection theory in the tautological ring moduli spaces of curves. The subject has its origin in enumerative geometry and has been revolutionized by the celebrated Witten-Kontsevich theorem connecting intersection theory to KdV integrable hierarchy. In the 1990s, Faber proposed a series of remarkable conjectures about the structure of the tautological ring, which has been a major driving force in our understanding of moduli spaces of curves. I will talk about our work (joint with Prof. K. Liu) on recursion formulas of intersection numbers and their applications to Faber’s conjecture. I will also briefly introduce the recent influential work of Eynard and Orantin in random matrix theory, which gives a unifying recursion formalism for many problems in intersection theory.

Research Area