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SUMMARY:Mirror symmetry for homogeneous varieties. - Clelia Pech (Kent)
DTSTART:20161116T141500Z
DTEND:20161116T151500Z
UID:TALK67381@talks.cam.ac.uk
CONTACT:Dr. J Ross
DESCRIPTION:In this talk reporting on joint work with K. Rietsch and L. Wi
 lliams\, I will explain a new version of the construction by Rietsch of a 
 mirror for some varieties with a homogeneous Lie group action. The varieti
 es we study include quadrics and Lagrangian Grassmannians (i.e.\, Grassman
 nians of Lagrangian vector subspaces of a symplectic vector space). The mi
 rror takes the shape of a rational function\, the superpotential\, defined
  on a Langlands dual homogeneous variety. I will show that in the mirror m
 anifold has a particular combinatorial structure called a cluster structur
 e\, and that the superpotential is expressed in coordinates dual to the co
 homology classes of the original variety.\n\nI will also explain how these
  properties lead to new relations in the quantum cohomology\, and a conjec
 tural formula expressing solutions of the quantum differential equation fo
 r LG(n) in terms of the superpotential. If time allows\, I will also expla
 in how these results should extend to a larger family of homogeneous space
 s called `cominuscule homogeneous spaces'. 
LOCATION:CMS MR13
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