Publications

Sebastian Debus, Philippe Moustrou, Cordian Riener, Hugues Verdure (2022). The poset of Specht ideals for hyperoctahedral groups. Arxiv.

Mario Kummer, Cordian Riener (2022). Equivariant algebraic and semi-algebraic geometry of infinite affine space. arXiv:2203.11921.

Cordian Riener, Robin Schabert (2022). Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions. arXiv:2203.08727.

Evelyne Hubert, Tobias Metzlaff, Cordian Riener (2022). Polynomial description for the T-Orbit Spaces of Multiplicative Actions. arxiv:2203.13152.

Saugata Basu, Cordian Riener (2021). Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets. Foundations of Computational Mathematics.

Philippe Moustrou, Helen Naumann, Cordian Riener, Thorsten Theobald, Hugues Verdure (2021). Symmetry reduction in AM/GM-based optimization. SIAM J. Optimization.

Grigoriy Blekherman, Cordian Riener (2021). Symmetric nonnegative forms and sums of squares. Discrete & Computational Geometry.

Philippe Moustrou, Cordian Riener, Hugues Verdure (2021). Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations. Journal of Symbolic Computation.

Ragni Piene, Cordian Riener, Boris Shapiro (2021). Return of the plane evolute. arXiv:2110.11691.

Istvan Miklos, Cordian Riener (2021). # P-hardness proofs of matrix immanants evaluated on restricted matrices. arXiv preprint arXiv:2103.04934.

Sebastian Debus, Cordian Riener (2020). Reflection groups and cones of sums of squares. arXiv preprint arXiv:2011.09997.

Saugata Basu, Cordian Riener (2020). On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities. International Mathematics Research Notices.

Grigoriy Blekherman, Mario Kummer, Cordian Riener, Markus Schweighofer, Cynthia Vinzant (2020). Generalized eigenvalue methods for Gaussian quadrature rules. Annales Henri Lebesgue.

Tobias Friedl, Cordian Riener, Raman Sanyal (2018). Reflection groups, reflection arrangements, and invariant real varieties. Proceedings of the AMS.

Cordian Riener, Mohab Safey El Din (2018). Real root finding for equivariant semi-algebraic systems. International Symposium on Symbolic and Algebraic Computation.

Cordian Riener, Markus Schweighofer (2018). Optimization approaches to quadrature: new characterizations of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions. Journal of Complexity.

Saugata Basu, Cordian Riener (2018). On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms. Selecta Mathematica.

Cordian Riener, Nicolai Vorobjov (2017). On irreducible components of real exponential hypersurfaces. Arnold Mathematical Journal.

Saugata Basu, Cordian Riener (2017). Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets. Ordered Algebraic Structures and Related Topics, Contemporary Mathematics.

Saugata Basu, Cordian Riener (2017). Bounding the equivariant Betti numbers of symmetric semi-algebraic sets. Advances in Mathematics.

Cordian Riener (2016). Symmetric semi-algebraic sets and non-negativity of symmetric polynomials. Journal of Pure and Applied Algebra.

Paul Görlach, Cordian Riener, Tillmann Weißer (2016). Deciding positivity of multisymmetric polynomials. Journal of Symbolic Computation.

Cordian Riener, Thorsten Theobald, Lina Jansson Andrén, Jean B Lasserre (2013). Exploiting symmetries in SDP-relaxations for polynomial optimization. Mathematics of Operations Research.

Cordian Riener (2012). On the degree and half-degree principle for symmetric polynomials. Journal of Pure and Applied Algebra.

Alexander Kovačec, Salma Kuhlmann, Cordian Riener (2012). A note on extrema of linear combinations of elementary symmetric functions. Linear and Multilinear Algebra.

Cordian Benedikt Riener (2011). Symmetries in Semidefinite and Polynomial Optimization: Relaxations, Combinatorics, and the Degree Principle.

Cordian Riener, Thorsten Theobald (2008). Positive Polynome und semidefinite Optimierung. Jahresbericht der DMV.

Cordian Riener (2006). On extreme forms in dimension 8. Journal de théorie des nombres de Bordeaux.