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Mirror symmetry, integrable systems and the Gopakumar--Vafa correspondence for Clifford--Klein 3-manifolds

Presented by: 
Andrea Brini Imperial College London, CNRS (Centre national de la recherche scientifique)
Monday 10th April 2017 - 13:30 to 14:30
INI Seminar Room 1
I will report on recent progress on the Gopakumar--Ooguri--Vafa correspondence, relating quantum (Witten--Reshetikhin--Turaev) invariants of 3-manifolds and knots therein with curve-counting theories (Gromov--Witten/Donaldson--Thomas) of local Calabi--Yau threefolds, in the context of Seifert-fibred 3-manifolds. I will describe A- and B- model constructions for the correspondence in the broadest context where the standard form of the duality is expect to hold (spherical space forms), discuss the link with relativistic integrable systems and the Eynard--Orantin topological recursion, and present a rigorous proof of the B-model version of the correspondence via matrix model techniques. Implications for refined invariants, orbifold GW theory, and an allied class of Frobenius manifolds and 2D-Toda reductions will be also discussed time permitting.

Based on joint work with G. Borot and further work in progress.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons