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SUMMARY:Mirror symmetry\, integrable systems and the Gopakumar--Vafa corre
 spondence for Clifford--Klein 3-manifolds - Andrea Brini (Imperial College
  London\; CNRS (Centre national de la recherche scientifique))
DTSTART:20170410T123000Z
DTEND:20170410T133000Z
UID:TALK71877@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:I will report on recent progress on the Gopakumar--Ooguri--Vaf
 a correspondence\, relating quantum (Witten--Reshetikhin--Turaev) invarian
 ts 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 constructi
 ons for the correspondence in the broadest context where the standard form
  of the duality is expect to hold (spherical space forms)\, discuss the li
 nk with relativistic integrable systems and the Eynard--Orantin topologica
 l recursion\, and present a rigorous proof of the B-model version of the c
 orrespondence via matrix model techniques. Implications for refined invari
 ants\, orbifold GW theory\, and an allied class of Frobenius manifolds and
  2D-Toda reductions will be also discussed time permitting.<br><br>Based o
 n joint work with G. Borot and further work in progress.<br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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