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Abstract |
The main protagonist of this talk is the Fukaya category of a
(type A) "Landau-Ginzburg model", i.e., a symplectic fibration over the
complex plane. We will outline one definition of this category, and
describe a pair of natural functors relating it to the Fukaya category
of the fiber. These functors are of particular interest in homological
mirror symmetry, where they correspond to inclusion and restriction
functors between derived categories of coherent sheaves on a variety and
a hypersurface inside it. This leads in particular to a proof of
homological mirror symmetry for general hypersurfaces in toric
varieties. The talk will be mostly expository; the non-expository parts
are joint work with Mohammed Abouzaid on one hand, and the thesis work
of Maxim Jeffs on the other hand. |
