Mirror symmetry for minuscule flag varieties

Nicolas Templier
Cornell
March 15, 2017
Abstract: We prove cases of Rietsch mirror conjecture that the A-model of projective
homogeneous varieties is isomorphic to the B-model of its mirror, which is a partially
compactified Landau--Ginzburg model constructed from Lie theory and geometric crystals. The
conjecture relates to deep objects in algebraic combinatorics. Our method of proof comes from
Langlands reciprocity, and consists in identifying the quantum connection as Galois and the
crystal as automorphic. I will mention further potential interactions between symplectic
geometry and number theory that it suggests. Work with Thomas Lam.
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