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math.CO2026
A note on bounded ratios
Lorenzo Baldi, Mario Kummer
We prove that the set of bounded ratios $\BR(X)$ on a semialgebraic set is the convex cone of linear forms that are nonnegative on the tropicalization $\trop(X)…
math.CO2026
Lorentzian polynomials and matroids over triangular hyperfields 2: Analytic aspects
Matthew Baker, June Huh, Mario Kummer +1
Brändén and Huh showed that Lorentzian polynomials unify Hodge-Riemann relations in combinatorics: their supports are M-convex, and every M-convex set supports a Lorentzian polynom…
math.AG2026
Ulrich sheaves and determinantal representations for higher secant varieties of curves
Daniele Agostini, Mario Kummer, Jinhyung Park
We show that higher secant varieties of smooth projective curves have symmetric admissible determinantal representations with symmetric Ulrich sheaves of rank one if the embedding…