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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, October 26, 2023 - 3:30pm

Jonathan Boretsky



Drexel University

Korman 245

The flag variety of rank r = (r1,...,rk) has points corresponding to collections of subspaces (V1,...,Vk) with Vi of dimension ri such that Vi is contained in Vi+1. It can be embedded into a multi-projective space, where it is cut out by the incidence Plücker relations. We explore two extensions of this variety: First, we study the nonnegative flag variety, which corresponds to a subset of the flag variety consisting of flags that can be represented by totally positive matrices. Second, we study the tropicalization of the flag variety and, more specifically, its nonnegative part. In both cases, we provide equivalent descriptions of these spaces for flag varieties of rank r = (aa+1, ..., b), where r consists of consecutive integers. We also explore descriptions of the nonnegative tropical flag variety in terms of polytopal subdivisions. This talk is based on joint work with Chris Eur and Lauren Williams.