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On the Hodge-GUE correspondence

Posted in
Di Yang
Mon, 2017-11-27 17:30 - 18:30
MPIM Lecture Hall

We discuss the recent Hodge--GUE correspondence conjecture on an explicit
relationship between special cubic Hodge integrals over the moduli space of stable
algebraic curves and enumeration of ribbon graphs with even valencies. We sketch
a proof of this conjecture based on the Virasoro constraints. We also discuss the
conjectural relationship between the cubic Hodge integrals satisfying the local
Calabi--Yau condition and the Bogoyavlensky--Toda hierarchy (aka fractional
KdV). The talk is based on a series of joint works with B. Dubrovin, S.-Q. Liu
and Y. Zhang.

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