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Geometry and Physics Seminar

Homological mirror symmetry for Grassmannians: rectangles

Marco Castronovo, Rutgers University

Location:  Serin Lab E372
Date & time: Thursday, 27 September 2018 at 1:30PM - 2:30PM

ABSTRACT:  Marsh-Rietsch proposed Landau-Ginzburg mirrors for the complex Grassmannians Gr(k,n), building on Peterson's work on the quantum cohomology of flag varieties. We confirm that they satisfy homological mirror symmetry when n=p prime. The proof describes an explicit correspondence between Lagrangian branes generating the Fukaya category of Gr(k,p) and sheaves generating the category of singularities of the mirror potential. The assumption n=p forces the singularities to lie in a special cluster chart of the mirror, that we call rectangular, by an argument that combines arithmetic properties of sums of roots of unity and Stanley's hook-content formula for the number of semi-standard tableaux on a Young diagram.

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