GOCC 3/12/2025 "Polynomial inequalities for cone-volumes of polytopes"
Автор: GOCC Combinatorics
Загружено: 2025-03-13
Просмотров: 122
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Speaker: Tom Baumbach (TU Berlin)
Abstract: Motivated by the logarithmic Minkowski problem, we study the cone-volume set C(U) associated with a given matrix U = (u_1,...,u_m) in R^{n x m}. This set consists of all cone-volume vectors of polytopes of the form P(U, b) = { x ∈ R^n | Uᵀx ≤ b }, where b \geq 0. We show that C(U) is a semialgebraic set, extending a previous planar result by Stancu. Furthermore, we introduce the subspace concentration polytope P_scc(U), which provides a geometric representation of subspace concentration conditions for a finite discrete Borel measure on the sphere. Interestingly, this polytope turns out to be a matroid base polytope. The two sets P_scc(U) and C(U) also offer a new geometric perspective on the discrete logarithmic Minkowski problem.
This is joined work with Martin Henk.
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