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Exterior algebras and local mirror symmetry

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If you have a question about this talk, please contact Dhruv Ranganathan.

In mirror symmetry, points in a variety correspond to Lagrangian tori in the mirror symplectic manifold. In the absence of “quantum corrections” the Ext-algebra of a point is equated with the cohomology algebra of the corresponding torus – both are simply exterior algebras – but in general one has to consider deformations of this picture. In this talk I’ll introduce the localised mirror functor of Cho, Hong and Lau, which translates deformations of this sort into the algebro-geometric language of matrix factorisations, and show how this leads to an easy proof that local mirror symmetry near a (monotone) Lagrangian torus is essentially tautological.

This talk is part of the Algebraic Geometry Seminar series.

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