Permutahedral Subdivisions and Class Formulas from Coxeter Elements

Explore a mathematical lecture from the Workshop on Combinatorics of Enumerative Geometry where Melissa Sherman-Bennett from the University of California, Davis delves into regular subdivisions of the permutahedron corresponding to Coxeter elements in the symmetric group. Learn about Bruhat interval subdivisions, where each face represents the convex hull of permutations in a Bruhat interval, and discover their connection to cones in the positive tropical flag variety through the work of Joswig-Loho-Luber-Olarte and Boretsky-Eur-Williams. Examine how these subdivisions indexed by Coxeter elements correspond to maximal cones and understand new formulas for the class of the permutahedral variety as a sum of Richardson classes in the cohomology ring of the flag variety, developed through collaborative research with Allen Knutson and Mario Sanchez.