Program
Introduction to the Eynard-Orantin invariants
Student No.:50
Time:【updated】Tue 13:00-14:50/Fri 10:10-12:00, 2015-05-29 ~ 2015-06-26(No classes on June 2/5)
Instructor:Chiu-Chu Melissa Liu  [Columbia University]
Place:【updated】Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2015-5-29
Ending Date:2015-6-26
 

Description:

 

In 2007, theoretical physicists B. Eynard and N. Orantin define an infinite sequence of invariants, now know as Eynard-Orantin invariants, for an arbitrary algebraic curve. These invariants are constructed to coincide with the topological expansion of a matrix formal integral when the curve is the large N limit of the matrix model's spectral curve. We will give an exposition of the work of Eynard-Orantin, and relate Eynard-Orantin invariants to intersection theory of moduli of stable curves and stable maps.

 

 

Prerequisite:

 

Basic theory of Riemann surfaces.

 

 

Reference:

 
(1) B. Eynard, N. Orantin, “Invariants of algebraic curves and topological expansion,” Commun. Number Theory Phys. 1 (2007) no.2, 347-352
 
(2) B. Eynard, “Invariants of spectral curves and intersection theory of moduli spaces of complex curves,” Commun. Number Theory Phys. 8 (2014), no.3, 541-588.
 
(3) P. Dunin-Barkowski, N. Orantin, S. Shadrin, L. Spitz, “Identification of the Givental formula with the spectral curve topological recursion procedure,” Comm. Math. Phys. 328 (2014), no.2, 669-700