Papers by the principal investigator, the project's postdocs and PhD students, 2018–2026. Where a paper has appeared in a journal, the journal is given; the remaining preprints are listed with their arXiv number.

2026

• J. Acevedo, G. Blekherman, S. Debus, C. Riener. The wonderful geometry of the Vandermonde map. Foundations of Computational Mathematics 26(4), 2005–2051.
• S. Debus, C. Riener, R. Schabert. Slices of stable polynomials and connections to the Grace–Walsh–Szegő theorem. Journal of Symbolic Computation 133, 102488.
• F. Galuppi, P. Santarsiero, D. A. Torrance, E. Teixeira Turatti. Geometry of first nonempty Terracini loci. Communications in Contemporary Mathematics 28(4), 2550053.
• I. Miklós, C. Riener. #P-hardness proofs of matrix immanants evaluated on restricted matrices. Theoretical Computer Science 1062, 115660.
• P. Moustrou, C. Riener, R. Schabert. Constructively describing orbit spaces of finite groups by few inequalities. Journal of Symbolic Computation 132, 102471.
• C. Riener, E. Teixeira Turatti. Quadrature rules with few nodes supported on algebraic curves. Journal of Complexity 96, 102067.

2025

• J. Acevedo, G. Blekherman, S. Debus, C. Riener. Symmetric nonnegative functions, the tropical Vandermonde cell and superdominance of power sums. Collectanea Mathematica, doi:10.1007/s13348-025-00481-z.
• S. Debus, C. Goel, S. Kuhlmann, C. Riener. On nonnegative invariant quartics in type A. Journal of Symbolic Computation 128, 102393.
• E. Hubert, T. Metzlaff, P. Moustrou, C. Riener. Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs. Mathematical Programming 213, 517–573.
• M. Korda, V. Magron, R. Ríos-Zertuche. Convergence rates for sums-of-squares hierarchies with correlative sparsity. Mathematical Programming 209, 435–473.
• M. Kummer, C. Riener. Equivariant algebraic and semi-algebraic geometry of infinite affine space. Journal of Algebra 666, 28–46.
• P. Moustrou, C. Riener, T. Theobald, H. Verdure. Symmetric SAGE and SONC forms, exactness and quantitative gaps. Journal of Symbolic Computation 127, 102374.
• R. Piene, C. Riener, B. Shapiro. Return of the plane evolute. Annales de l'Institut Fourier 75(4), 1685–1751.
• C. Riener, J. Rolfes, F. Vallentin. A semidefinite programming hierarchy for covering problems in discrete geometry. Numerical Algebra, Control and Optimization, doi:10.3934/naco.2025015.
• C. Riener, R. Schabert, T. X. Vu. Deciding connectivity in symmetric semi-algebraic sets. Journal of Symbolic Computation, to appear (arXiv:2503.12275).

2024

• E. Hubert, T. Metzlaff, C. Riener. Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description. SIAM Journal on Applied Algebra and Geometry 8(3), 612–649.
• C. Riener, R. Schabert. Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions. Journal of Pure and Applied Algebra 228(5), 107552.
• C. Riener, R. Schabert, T. X. Vu. Connectivity in symmetric semi-algebraic sets. ISSAC 2024, 162–169 (best PhD paper award).
• L. Sodomaco, E. Teixeira Turatti. The span of singular tuples of a tensor beyond the boundary format. Journal of Symbolic Computation 120, 102230.

2023

• S. Debus, C. Riener. Reflection groups and cones of sums of squares. Journal of Symbolic Computation 119, 112–144.
• S. Debus, P. Moustrou, C. Riener, H. Verdure. The poset of Specht ideals for hyperoctahedral groups. Algebraic Combinatorics 6(6), 1593–1619.
• J.-C. Faugère, G. Labahn, M. Safey El Din, É. Schost, T. X. Vu. Computing critical points for invariant algebraic systems. Journal of Symbolic Computation 116, 365–399.
• F. Galuppi, F. Gesmundo, E. Teixeira Turatti, L. Venturello. Characteristic polynomials and eigenvalues of tensors. arXiv:2308.10957.
• G. Labahn, C. Riener, M. Safey El Din, É. Schost, T. X. Vu. Faster real root decision algorithm for symmetric polynomials. ISSAC 2023, 452–460.
• P. Moustrou, C. Riener, H. Verdure. Symmetries in polynomial optimization. In Polynomial Optimisation, Moments, and Applications, Springer Optimization and Its Applications 206, 53–111.
• G. Óturai, C. Riener, S. E. Martiny. Attitudes towards mathematics, achievement, and drop-out intentions among STEM and non-STEM students in Norway. International Journal of Educational Research Open 4, 100230.

2022

• S. Basu, C. Riener. Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets. Foundations of Computational Mathematics 22, 1395–1462.
• E. Hubert, T. Metzlaff, P. Moustrou, C. Riener. T-orbit spaces of multiplicative actions and applications. ACM Communications in Computer Algebra 56(2), 72–75.
• G. Labahn, V. Neiger, T. X. Vu, W. Zhou. Rank-sensitive computation of the rank profile of a polynomial matrix. ISSAC 2022, 351–360.
• P. Moustrou, H. Naumann, C. Riener, T. Theobald, H. Verdure. Symmetry reduction in AM/GM-based optimization. SIAM Journal on Optimization 32(2), 765–785.
• T. X. Vu. Computing critical points for algebraic systems defined by hyperoctahedral invariant polynomials. ISSAC 2022, 167–175.

2021

• G. Blekherman, C. Riener. Symmetric nonnegative forms and sums of squares. Discrete & Computational Geometry 65, 764–799.
• M. Dostert, D. de Laat, P. Moustrou. Exact semidefinite programming bounds for packing problems. SIAM Journal on Optimization 31(2), 1433–1458.
• M. Dutour Sikirić, D. A. Madore, P. Moustrou, F. Vallentin. Coloring the Voronoi tessellation of lattices. Journal of the London Mathematical Society 104(3), 1135–1171.
• P. Moustrou, C. Riener, H. Verdure. Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations. Journal of Symbolic Computation 107, 106–121.

2020

• S. Basu, C. Riener. On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities. International Mathematics Research Notices 2020(7), 2054–2113.
• G. Blekherman, M. Kummer, C. Riener, M. Schweighofer, C. Vinzant. Generalized eigenvalue methods for Gaussian quadrature rules. Annales Henri Lebesgue 3, 1327–1341.

2019

• C. Bachoc, T. Bellitto, P. Moustrou, A. Pêcher. On the density of sets avoiding parallelohedron distance 1. Discrete & Computational Geometry 62(3), 497–524.

2018

• C. Riener, M. Safey El Din. Real root finding for equivariant semi-algebraic systems. ISSAC 2018, 335–342.
• C. Riener, M. Schweighofer. 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 45, 22–54.