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Center & Programs Conferences Conference and Winter School on: Tropical Geometry, Berkovich spaces and mirror symmetry
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"Mirror symmetry via non-archimedean geometry"(Lecture IV-1.)
SPEAKER  |  Mohammed Abouzaid
INSTITUTE  |  (Columbia University)
DATE  |  February 24(Wed), 2016
TIME  |  09:30
PLACE  |  Rm 1503(Bldg#I,5th), Korea Institute for Advanced Study, South Korea
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ABSTRACT  |  I will describe a program, building on ideas of Kontsevich-Soibleman and Fukaya, for proving Homological mirror symmetry by associating to symplectic manifolds equipped with torus fibrations a rigid-analytic space, which is a moduli space of rank-1 local systems on the torus fibres, and which ends up being the mirror space. The key insights required to implements such a constructions are: (1) wall crossing maps from moduli spaces of holomorphic discs, giving transition functions between different affinoid covers of the mirror (2) constructions of objects of the Fukaya category associated to singular fibres and (3) a TQFT argument for proving the non-degeneracy of the mirror functor.
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