Seminario Teoría de Grupos
The strong exchange property for Coxeter matroids
Ponente: Aram Dermenjiann (Universidad de Sevilla)Fecha: miércoles 19 de noviembre de 2025 - 16:00Lugar: Aula Naranja, ICMAT
Resumen:
This talk assumes no prior knowledge for any of the terms mentioned in this abstract. Matroids are a combinatorial structure that abstracts linear independence. They have a deep connection with Grassmannians, the variety of subspaces of a vector space cut out by the Plücker equations. Grassmannians and matroids are inherently 'type A' objects and have generalizations to other root systems giving rise to what is known as Coxeter matroids. As such, one can generalize (through representation theory) these Grassmannians and Plücker equations to other Coxeter types using miniscule varieties and equations that define the quotient G/P of a simply connected complex Lie Group G by a maximal parabolic subgroup P with a miniscule fundamental representation. In addition, Borovik, Gelfand and White give a description of a strong exchange property for Coxeter matroids. It turns out there is a strong link between the strong exchange property and the tropicalization of the equations that define G/P. In this talk, we describe this link through representation theory, tropical geometry and polytope theory. (This is joint work with Kieran Calvert, Alex Fink and Ben Smith).
