Publications

Jose Acevedo, Grigoriy Blekherman, Sebastian Debus, Cordian Riener (2023). The wonderful geometry of the Vandermonde map. arXiv preprint arXiv:2303.09512.

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Sebastian Debus, Philippe Moustrou, Cordian Riener, Hugues Verdure (2023). The poset of Specht ideals for hyperoctahedral groups. Algebraic Combinatorics.

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Philippe Moustrou, Cordian Riener, Hugues Verdure (2023). Symmetries in polynomial optimization. Polynomial Optimisation, Moments, and Applications.

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Philippe Moustrou, Cordian Riener, Theosten Theobald, Hugues Verdure (2023). Symmetric SAGE and SONC forms, exactness and quantitative gaps. arXiv preprint arXiv:2312.10500.

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Sebastian Debus, Cordian Riener (2023). Reflection groups and cones of sums of squares. Journal of Symbolic Computation.

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Michal Kočvara, Bernard Mourrain, Cordian Riener (2023). Polynomial Optimisation, Moments, and Applications. Springer Optimization and Its Applications.

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Evelyne Hubert, Tobias Metzlaff, Philippe Moustrou, Cordian Riener (2023). Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs.

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George Labahn, Cordian Riener, Mohab Safey El Din, Éric Schost, Thi Xuan Vu (2023). Faster real root decision algorithm for symmetric polynomials. International Symposium on Symbolic and Algebraic Computation 2023.

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Gabriella Óturai, Cordian Riener, Sarah E Martiny (2023). Attitudes towards mathematics, achievement, and drop-out intentions among STEM and Non-STEM students in Norway. International Journal of Educational Research Open.

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Cordian Riener, Jan Rolfes, Frank Vallentin (2023). A semidefinite programming hierarchy for covering problems in discrete geometry. arXiv preprint arXiv:2312.11267.

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

DOI

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

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

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

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Gunnar Fløystad, Satoshi Murai, Cordian Riener, Kohji Yanagawa (2022). MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties. Oberwolfach Reports.

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Cordian Riener, Istvan Miklos (2022). # P-hardness of matrix immanants on restricted matrices.. 2022 Spring Central Sectional Meeting.

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

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

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

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

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

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Cordian Riener, Sebastian Debus (2021). Polynomial opzimization problems invariant by finite reflection groups. 2021 Joint Mathematics Meetings (JMM).

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

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

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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.

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

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

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

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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.

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

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

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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.

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

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

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

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Saugata Basu, Cordian Riener (2016). Bounds on the individual Betti numbers of complex varieties, stability and algorithms. arXiv preprint arXiv:1606.04069.

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

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

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

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

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

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

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