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The coherent-constructible correspondence for toric varieties

SPEAKER: David Treumann

TITLE: The coherent-constructible correspondence for toric varieties

ABSTRACT This is a talk on joint work with Bohan Fang, Chiu-Chu Melissa Liu, and Eric Zaslow. I will discuss a triangle of equivalences we have constructed between a category of equivariant coherent sheaves on a toric variety, a category of polyhedrally-constructible sheaves on a real vector space, and a Fukaya category of Lagrangian branes in a symplectic vector space. Many famous results of toric geometry admit interpretations in terms of this coherent-constructible correspondence, and the connection to the Fukaya category can be seen as a verification–for toric varieties–of an equivariant form of Kontsevich’s homological mirror symmetry conjectures