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



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.





Basic theory of Riemann surfaces.




(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