MIT-Harvard-MSR Combinatorics Seminar

Wednesday, October 12, 2022 at 4:15pm to 5:15pm

MIT-Department of Mathematics, Room 2-132

Speaker:  Melissa Sherman-Bennett  (MIT)

Title:  Cluster structure on braid varieties from 3D plabic graphs


Braid varieties are smooth irreducible affine varieties associated to any positive braid.  Their cohomology is expected to contain information about the Khovanov-Rozansky homology of a related link.  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.  Seeds for these cluster algebras come from "3D plabic graphs", which are bicolored graphs embedded in a 3-dimensional ball and generalized postnikov's plabic graphs for positroid varieties.


Event Type


Events By Interest


Events By Audience

MIT Community

Events By School

School of Science


Department of Mathematics
Contact Email

Add to my calendar

Recent Activity