- Series
- Combinatorics Seminar
- Time
- Friday, April 25, 2025 - 3:15pm for 1 hour (actually 50 minutes)
- Location
- 1214 in the U A Whitaker Biomedical Engr. building
- Speaker
- Colin Defant – Harvard University – colindefant@gmail.com – https://sites.google.com/view/colin-defant/home
- Organizer
- Jiaxi Nie
Using the theory of total linear stability for Dynkin quivers and an interplay between the Bruhat order and the noncrossing partition lattice, we define a family of triangulations of the permutohedron indexed by Coxeter elements. Each triangulation is constructed to give an explicit homotopy between two complexes (the Salvetti complex and the Bessis--Brady--Watt complex) associated to two different presentations of the corresponding braid group (the standard Artin presentation and Bessis's dual presentation). Our triangulations have several notable combinatorial properties. In addition, they refine similar Bruhat interval polytope decompositions of Knutson, Sanchez, and Sherman-Bennett. This is based on joint work with Melissa Sherman-Bennett and Nathan Williams.