3 papers
math.AG2026
Any-dimensional Positivstellensätze for symmetric functions
Sebastian Debus, Robin Schabert
Positivstellensätze provide certificates of positivity for polynomials. Extending these certificates to symmetric functions, uniformly across all dimensions, presents structural c…
math.AG2025
Slices of Stable Polynomials and Connections to the Grace-Walsh-SzegÅ theorem
Sebastian Debus, Cordian Riener, Robin Schabert
Univariate polynomials are called stable with respect to a domain if all of their roots lie in . We study linear slices of the space of stable univariate polynomials with re…
cs.SC2025
Deciding Connectivity in Symmetric Semi-Algebraic Sets
Cordian. Riener, Robin Schabert, Thi Xuan Vu
A semi-algebraic set is a subset of defined by a finite collection of polynomial equations and inequalities. In this paper, we investigate the problem of determining…