82 citations · 169 across the 34 of their papers we have counts for
43 papers
Diagonal Specht ideals and their varieties
Anna Escofet, Cordian Riener, Hugues Verdure
We study the diagonal Specht ideals , , generated by the -isoty…
Eigenvalues of locally positive semidefinite matrices: Non-convexity and Geometry
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +2
A real symmetric matrix is called -locally positive semidefinite if all of its principal submatrices are positive semidefinite. We investigate the spectral geometry…
Symmetric and Isotypic Hilbert Series for Symmetric Ideals
Henri Breloer, Cordian Riener
An ideal in a polynomial ring is symmetric if it is invariant under any permutation of variables. In this paper, we define and study the symmetric and isotypic Hilbert series for s…
Quadrature rules with few nodes supported on algebraic curves
Cordian Riener, Ettore Teixeira Turatti
We investigate quadrature rules for measures supported on real algebraic and rational curves, focusing on the {odd-degree} case \(2s-1\). Adopting an optimization viewpoint, we min…
Symbolic Computation with Symmetric Polynomials in Real Algebraic Geometry
Cordian Riener, Thi Xuan Vu
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inhere…
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…
Symmetric nonnegative functions, the tropical Vandermonde cell and superdominance of power sums
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +1
We study nonnegative and sums of squares symmetric (and even symmetric) functions of fixed degree. We can think of these as limit cones of symmetric nonnegative polynomials and sym…
Constructively describing orbit spaces of finite groups by few inequalities
Philippe Moustrou, Cordian Riener, Robin Schabert
Let be a finite group acting linearly on . A celebrated Theorem of Procesi and Schwarz gives an explicit description of the orbit space as a…
Connectivity in Symmetric Semi-Algebraic Sets
Cordian Riener, Robin Schabert, Thi Xuan Vu
Semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities. In this paper, we consider the problem of deciding whether two given points in a…
On nonnegative invariant quartics in type A
Sebastian Debus, Charu Goel, Salma Kuhlmann +1
The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type A. As a first step to a classification…
Slices of Stable Polynomials and Connections to the Grace-Walsh-Szegő 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…
A semidefinite programming hierarchy for covering problems in discrete geometry
Cordian Riener, Jan Rolfes, Frank Vallentin
In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed prim…
Symmetric SAGE and SONC forms, exactness and quantitative gaps
Philippe Moustrou, Cordian Riener, Thorsten Theobald +1
The classes of sums of arithmetic-geometric exponentials (SAGE) and of sums of nonnegative circuit polynomials (SONC) provide nonnegativity certificates which are based on the ineq…
Faster real root decision algorithm for symmetric polynomials
George Labahn, Cordian Riener, Mohab Safey El Din +2
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the a…
Symmetries in polynomial optimization
Philippe Moustrou, Cordian Riener, Hugues Verdure
This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SO…
Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
Evelyne Hubert, Tobias Metzlaff, Philippe Moustrou +1
Trigonometric polynomials are usually defined on the lattice of integers.We consider the larger class of weight and root lattices with crystallographic symmetry.This article gives…
The Wonderful Geometry of the Vandermonde map
Jose Acevedo, Grigoriy Blekherman, Sebastian Debus +1
We study the geometry of the image of the nonnegative orthant under the power-sum map and the elementary symmetric polynomials map. After analyzing the image in finitely many varia…
The poset of Specht ideals for hyperoctahedral groups
Sebastian Debus, Philippe Moustrou, Cordian Riener +1
Specht polynomials classically realize the irreducible representations of the symmetric group. The ideals defined by these polynomials provide a strong connection with the combinat…
Equivariant algebraic and semi-algebraic geometry of infinite affine space
Mario Kummer, Cordian Riener
We study -orbit closures of not necessarily closed points in the Zariski spectrum of the infinite polynomial ring $\mathbb{C}[x_{ij}:\, i\in\mathbb{N},\,j\in[…
Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description
Evelyne Hubert, Tobias Metzlaff, Cordian Riener
The Weyl group of a crystallographic root system has a nonlinear action on the compact torus. The orbit space of this action is a compact basic semi-algebraic set. We present a pol…
Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions
Cordian Riener, Robin Schabert
A real univariate polynomial of degree is called hyperbolic if all of its roots are on the real line. Such polynomials appear quite naturally in different applications, for…
Return of the plane evolute
Ragni Piene, Cordian Riener, Boris Shapiro
Below we consider the evolutes of plane real-algebraic curves and discuss some of their complex and real-algebraic properties. In particular, for a given degree , we provid…
#P-hardness proofs of matrix immanants evaluated on restricted matrices
Istvan Miklos, Cordian Riener
We establish the -hardness of computing a broad class of immanants, even when restricted to specific categories of matrices. Concretely, we prove that computing -immanants…
Symmetry reduction in AM/GM-based optimization
Philippe Moustrou, Helen Naumann, Cordian Riener +2
The arithmetic mean/geometric mean-inequality (AM/GM-inequality) facilitates classes of non-negativity certificates and of relaxation techniques for polynomials and, more generally…