7 papers
Nonlinear Kalman varieties
Flavio Salizzoni, Luca Sodomaco, Julian Weigert
We study the locus of square matrices having at least one eigenvector on a prescribed algebraic variety . When is a linear subspace, this data locus is known as the Kalman v…
Geometry of Adjoint Hypersurfaces for Polytopes
Clemens Brüser, Julian Weigert
In this article we prove that the adjoint polynomial of arbitrary convex polytopes is up to scaling uniquely determined by vanishing to the right order on the polytopes residual ar…
Toric extensions of Pólya's theorem
Lorenzo Baldi, Rainer Sinn, Máté L. Telek +1
The classical version of Pólya's theorem provides a simple method for certifying that a homogeneous polynomial of degree d is strictly copositive, that is, it takes only positive…
Nonlinear Rayleigh quotient optimization
Flavio Salizzoni, Luca Sodomaco, Julian Weigert
Rayleigh quotient minimization deals with optimizing a quadratic homogeneous function over a sphere. Its critical points correspond to the normalized eigenvectors of the symmetric…
Complete monotonicity of log-functions
Rourou Ma, Julian Weigert
In this article we investigate the property of complete monotonicity within a special family of functions in variables involving logarithms. The main result of…
Equivariant Tutte Polynomial
Mario Bauer, MatÄj Doležálek, Magdaléna MiÅ¡inová +2
We use the equivariant cohomology ring of the permutohedral variety to study matroids and their invariants. Investigating the pushforward of matroid Chern classes defined by A. Ber…