Cordian Riener

Publications

Journal articles, refereed conference papers, books, and selected preprints. Continuously updated lists live on arXiv, Google Scholar, and dblp.

2026

  1. The wonderful geometry of the Vandermonde map
    with J. Acevedo, G. Blekherman, and S. Debus
    Foundations of Computational Mathematics 26, 2005–2051 doiarXiv
  2. Quadrature rules with few nodes supported on algebraic curves
    with E. Teixeira Turatti
    Journal of Complexity 96, 102067 doiarXiv
  3. Slices of stable polynomials and connections to the Grace–Walsh–Szegő theorem
    with S. Debus and R. Schabert
    Journal of Symbolic Computation 133, 102488 doi
  4. Constructively describing orbit spaces of finite groups by few inequalities
    with P. Moustrou and R. Schabert
    Journal of Symbolic Computation 132, 102471 doi
  5. #P-hardness proofs of matrix immanants evaluated on restricted matrices
    with I. Miklós
    Theoretical Computer Science 1062, 115660 doi
  6. Symmetric and isotypic Hilbert series for symmetric ideals
    with H. Breloer
    preprint arXiv
  7. Eigenvalues of locally positive semidefinite matrices: non-convexity and geometry
    with J. Acevedo, G. Blekherman, S. Debus, and S. Lee
    preprint arXiv
  8. The Lie–Størmer Center
    with H. Z. Munthe-Kaas
    EMS Magazine 140, 37–39 doi
  9. Deciding connectivity in symmetric semi-algebraic sets
    with R. Schabert and T. X. Vu
    Journal of Symbolic Computation 138 arXiv
  10. A semidefinite programming hierarchy for covering problems in discrete geometry
    with J. Rolfes and F. Vallentin
    Numerical Algebra, Control and Optimization 16, 157–170 doiarXiv

2025

  1. Return of the plane evolute
    with R. Piene and B. Shapiro
    Annales de l’Institut Fourier 75, 1685–1751 doiarXiv
  2. Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
    with E. Hubert, T. Metzlaff, and P. Moustrou
    Mathematical Programming 213, 517–573 doi
  3. Symmetric SAGE and SONC forms, exactness and quantitative gaps
    with P. Moustrou, T. Theobald, and H. Verdure
    Journal of Symbolic Computation 127, 102374 doi
  4. On nonnegative invariant quartics in type A
    with S. Debus, C. Goel, and S. Kuhlmann
    Journal of Symbolic Computation 128, 102393 doi
  5. Symbolic computation with symmetric polynomials in real algebraic geometry
    with T. X. Vu
    survey chapter, preprint arXiv
  6. Symmetric nonnegative functions, the tropical Vandermonde cell and superdominance of power sums
    with J. Acevedo, G. Blekherman, and S. Debus
    Collectanea Mathematica doiarXiv
  7. Equivariant algebraic and semi-algebraic geometry of infinite affine space
    with M. Kummer
    Journal of Algebra 666, 28–46 doiarXiv

2024

  1. Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description
    with E. Hubert and T. Metzlaff
    SIAM Journal on Applied Algebra and Geometry 8, 612–649 doi
  2. Connectivity in symmetric semi-algebraic sets
    with R. Schabert and T. X. Vu
    Proceedings of ISSAC 2024, 162–169 doiarXiv
  3. Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions
    with R. Schabert
    Journal of Pure and Applied Algebra 228, 107552 arXiv

2023

  1. Reflection groups and cones of sums of squares
    with S. Debus
    Journal of Symbolic Computation 119, 112–144 doi
  2. Faster real root decision algorithm for symmetric polynomials
    with G. Labahn, M. Safey El Din, É. Schost, and T. X. Vu
    Proceedings of ISSAC 2023, 452–460 doiarXiv
  3. The poset of Specht ideals for hyperoctahedral groups
    with S. Debus, P. Moustrou, and H. Verdure
    Algebraic Combinatorics 6, 615–634 arXiv
  4. Symmetries in polynomial optimization
    with P. Moustrou and H. Verdure
    in: Polynomial Optimization, Moments, and Applications, Springer doi
  5. Polynomial Optimization, Moments, and Applications
    edited with M. Kočvara and B. Mourrain
    Springer Optimization and Its Applications, vol. 206 doi
  6. Attitudes towards mathematics, achievement, and drop-out intentions among STEM and non-STEM students in Norway
    with G. Óturai and S. E. Martiny
    International Journal of Educational Research Open 4, 100230 doi

2022

  1. Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets
    with S. Basu
    Foundations of Computational Mathematics 22, 1395–1462 doi
  2. Symmetry reduction in AM/GM-based optimization
    with P. Moustrou, H. Naumann, T. Theobald, and H. Verdure
    SIAM Journal on Optimization 32, 765–785 doi

2021

  1. Symmetric non-negative forms and sums of squares
    with G. Blekherman
    Discrete & Computational Geometry 65, 764–799 doi
  2. Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations
    with P. Moustrou and H. Verdure
    Journal of Symbolic Computation 107, 106–121 doi

2020

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

2018

  1. On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
    with S. Basu
    Selecta Mathematica 24, 3241–3281 doi
  2. 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
    with M. Schweighofer
    Journal of Complexity 45, 22–54 doi
  3. Real root finding for equivariant semi-algebraic systems
    with M. Safey El Din
    Proceedings of ISSAC 2018 doi
  4. Reflection groups, reflection arrangements, and invariant real varieties
    with T. Friedl and R. Sanyal
    Proceedings of the American Mathematical Society 146, 1031–1045 doi

2017

  1. Bounding the equivariant Betti numbers of symmetric semi-algebraic sets
    with S. Basu
    Advances in Mathematics 305, 803–855 doi
  2. Efficient algorithms for computing the Euler–Poincaré characteristic of symmetric semi-algebraic sets
    with S. Basu
    in: Ordered Algebraic Structures and Related Topics, Contemporary Mathematics 697 doi
  3. On irreducible components of real exponential hypersurfaces
    with N. Vorobjov
    Arnold Mathematical Journal 3, 423–443 doi

2016

  1. Bounds on the individual Betti numbers of complex varieties, stability and algorithms
    with S. Basu
    preprint arXiv
  2. Deciding positivity of multisymmetric polynomials
    with P. Görlach and T. Weißer
    Journal of Symbolic Computation 74, 603–616 doi
  3. Symmetric semi-algebraic sets and non-negativity of symmetric polynomials
    Journal of Pure and Applied Algebra 220, 2809–2815 doi

2013

  1. Exploiting symmetries in SDP-relaxations for polynomial optimization
    with T. Theobald, L. Jansson Andrén, and J. B. Lasserre
    Mathematics of Operations Research 38, 122–141 doi

2012

  1. On the degree and half-degree principle for symmetric polynomials
    Journal of Pure and Applied Algebra 216, 850–856 doi
  2. A note on extrema of linear combinations of elementary symmetric functions
    with A. Kovačec and S. Kuhlmann
    Linear and Multilinear Algebra 60, 219–224 doi

2011

  1. Symmetries in semidefinite and polynomial optimization: relaxations, combinatorics, and the degree principle
    PhD thesis, Goethe University Frankfurt

2008

  1. Positive Polynome und semidefinite Optimierung
    with T. Theobald
    Jahresbericht der DMV 110, 3–21

2006

  1. On extreme forms in dimension 8
    Journal de théorie des nombres de Bordeaux 18, 677–682 doi