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

Melissa Sherman-Bennett, Massachusetts Institute of Technology
Wednesday, November 16, 2022 - 3:30pm to 5:00pm
PDL C-38 and via Zoom Link:


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 and generalize Postnikov's plabic graphs for positroid varieties.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting:
Meeting ID: 915 4733 5974