Title:
Cluster gluings and open-string Schubert calculus
Abstract:
When is a gluing of affine schemes affine? I will state a conjectural answer when the pieces are tori, and the gluing maps are cluster mutations in the sense of Fomin-Zelevinsky. The combinatorics of Demazure weaves allows to prove the conjecture in interesting cases, notably those in which there are finitely many tori, as well as the simplest ones with infinitely many. This has applications to open-string Schubert calculus, i.e. computations of the Fukaya category of homogeneous manifolds G/P. Joint work with M. Gorsky, J. Simental, D. Speyer.
Eric Zaslow
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