|XXXII Workshop on Geometric Methods in Physics||30.06-6.07.2013|
Participants of Workshop
Participants of School
Matrix models topological recursion and Givental theory
Topological recursion for matrix models has appeared in the papers of Chekhov, Eynard, and Orantin, and it serves both as a very powerful computational tool and as a way to defines the correlation forms of a matrix model in a mathematically rigorous way.
We explain a version of the topological recursion procedure for a collection of isolated local germs of the spectral curve. Under some conditions we can identify the n-point functions computed from spectral curve with the Givental formula for the ancestor formal Gromov-Witten potential.
Using this identification one can deduce various relations of combinatorial problems to the intersection theory of the moduli spaces of curves. Examples include the Norbury-Scott conjecture on a particular spectral curve for the Gromov-Witten theory of $CP^1$, a new way to derive the ELSV formula for Hurwitz numbers, and a mathematical physics proof of the 2006 conjecture of Zvonkine that relates Hurwitz numbers with completed cycles to the intersection theory of the moduli spaces of $r$-spin structure.
The talk will follow my recent works with Dunin-Barkowski, Orantin, Spitz, and Zvonkine.
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