Cluster structures on type A braid varieties and 3D plabic graphs

Abstract: Braid varieties are smooth affine varieties associated to any positive braid. Special cases of braid varieties include Richardson varieties, double Bruhat cells, and double Bott-Samelson cells. Cluster algebras are a class of commutative rings with a rich combinatorial structure, introduced by Fomin and Zelevinsky. I'll discuss joint work with P. Galashin, T. Lam and D. Speyer in which we show the coordinate rings of braid varieties are cluster algebras, proving and generalizing a conjecture of Leclerc in the case of Richardson varieties. Seeds for these cluster algebras come from "3D plabic graphs", which are bicolored graphs embedded in a 3-dimensional ball that generalize Postnikov's plabic graphs for positroid varieties.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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