Tropical Positivity and Determinantal varieties

Abstract: A determinantal variety is the set of (d x n)-matrices of bounded rank. We study the tropicalization of the set of matrices with positive entries and bounded rank, i.e. the positive part of determinant varieties. Given such a (d x n)-matrix of fixed rank r, we can interpret the columns of the tropicalization of this matrix as n points in d-dimensional space, lying on a common r-dimensional tropical linear space. We consider such tropical point configurations, and introduce a combinatorial criterion to characterize configurations which can be obtained from the tropicalization of matrices with positive entries. No prior knowledge of tropical geometry will be assumed for this talk. This is based on joint work with Georg Loho and Rainer Sinn.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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