Exact Lagrangian tori in affine varieties

Abstract: We will discuss what is known and unknown about the existence of exact Lagrangian tori in smooth affine varieties. Based on homological mirror symmetry and computations of Hochschild cohomology, we prove the nonexistence of exact Lagrangian tori in a class of affine conic bundles over C^n, which cannot in general be embedded in the complement of ample divisors in smooth Fano varieties. This result should be regarded as evidence for the existence of dilations.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

Free Mathematics Seminar

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