Bilde av Riener, Cordian
Bilde av Riener, Cordian
Matematihka ja statistihka instituhtta +4777644090

Cordian Riener



I work in the field of Real Algebraic Geometry and its applications in Nonlinear Optimization. In this context I am interested in polynomial optimization, representation of positive polynomials by sums of squares, moment problems, quadrature formulas, algorithmic complexity, convex sets and semidefinite relaxation. I am also very much interested in philosophical questions related to mathematics and in particular determinism.

Please visit my Research Homepage for more details.


  • Ragni Piene, Cordian Riener, Boris Shapiro :
    Return of the evolute
    Annales de l'Institut Fourier 2024 FULLTEKST / ARKIV
  • Gabriella Óturai, Cordian Riener, Sarah Martiny :
    Attitudes towards mathematics, achievement, and drop-out intentions among STEM and Non-STEM students in Norway
    International Journal of Educational Research Open 2023 ARKIV / DOI
  • Sebastian Debus, Cordian Riener :
    Reflection groups and cones of sums of squares
    Journal of symbolic computation 2023 ARKIV / DOI
  • Cordian Benedikt Riener, Robin Leonid Schabert :
    Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions
    Journal of Pure and Applied Algebra 2023 ARKIV / DOI
  • Philippe Moustrou, Cordian Benedikt Riener, Hugues Verdure :
    Symmetries in Polynomial Optimization
    Springer 2023 DOI
  • Thi Xuan Vu, Mohab Safey el Din, George Labahn, Cordian Benedikt Riener, Éric Schost :
    Faster real root decision algorithm for symmetric polynomials
    Association for Computing Machinery 2023 DOI
  • Sebastian Debus, Philippe Moustrou, Cordian Benedikt Riener, Hugues Verdure :
    The poset of Specht ideals for hyperoctahedral groups
    Algebraic combinatorics 2023 ARKIV / DOI
  • Philippe Moustrou, Helen Naumann, Cordian Riener, Thorsten Theobald, Hugues Verdure :
    Symmetry Reduction in AM/GM-Based Optimization
    SIAM Journal on Optimization 2022 ARKIV / DOI
  • Saugata Basu, Cordian Riener :
    Vandermonde Varieties, Mirrored Spaces, and the Cohomology of Symmetric Semi-algebraic Sets
    Foundations of Computational Mathematics 2021 DOI
  • Philippe Moustrou, Cordian Riener, Hugues Verdure :
    Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations
    Journal of symbolic computation 2021 ARKIV / DOI
  • Grigoriy Blekherman, Cordian Riener :
    Symmetric Non-Negative Forms and Sums of Squares
    Discrete & Computational Geometry 2020 ARKIV / FULLTEKST / DOI
  • Grigoriy Blekherman, Mario Kummer, Cordian Riener, Markus Schweighofer, Cynthia Vinzant :
    Generalized eigenvalue methods for Gaussian quadrature rules
    Annales Henri Lebesgue (AHL) 2020 ARKIV / DOI
  • Cordian Riener, Markus 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 2018 DOI
  • Saugata Basu, Cordian Riener :
    On the Isotypic Decomposition of Cohomology Modules of Symmetric Semi-algebraic Sets: Polynomial Bounds on Multiplicities
    International Mathematics Research Notices (IMRN) 2018 ARKIV / DOI
  • Saugata Basu, Cordian Riener :
    On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
    Selecta Mathematica, New Series 2018 ARKIV / DOI
  • Tobias Friedl, Cordian Riener, Raman Sanyal :
    Reflection groups, arrangements, and invariant real varieties
    Proceedings of the American Mathematical Society 2018 ARKIV / DOI
  • Cordian Riener, Nicolai Vorobjov :
    On Irreducible Components of Real Exponential Hypersurfaces
    Arnold Mathematical Journal 2017 DOI
  • Saugata Basu, Cordian Riener :
    Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets
    Contemporary Mathematics 2017 DOI
  • Saugata Basu, Cordian Riener :
    Bounding the equivariant Betti numbers of symmetric semi-algebraic sets
    Advances in Mathematics 2017 DOI
  • Cordian Riener :
    Symmetric semi-algebraic sets and non-negativity of symmetric polynomials polynomials
    Journal of Pure and Applied Algebra 2016 DOI
  • Cordian Riener, Paul Görlach, Tillmann Weißer :
    Deciding positivity of multisymmetric polynomials
    Journal of symbolic computation 2016 DOI
  • Cordian Riener, Thorsten Theobald, Jean Bernard Lasserre, Lina Jansson Andrén :
    Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization
    Mathematics of Operations Research 2013 DOI
  • Cordian Riener :
    On the degree and half-degree principle for symmetric polynomials
    Journal of Pure and Applied Algebra 2012 DOI
  • Cordian Riener, Kovacec Alexander, Kuhlmann Salma :
    A Note on Extrema of Linear Combinations of Elementary Symmetric Functions
    Linear and multilinear algebra 2012
  • Cordian Riener, Thorsten Theobald :
    Positive Polynome und semidefinite Optimierung
    Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner) 2008
  • Cordian Riener :
    On extreme forms in dimension 8
    Journal de Théorie des Nombres de Bordeaux 2006
  • Michal Kočvara, Bernard Mourrain, Cordian Benedikt Riener :
    Polynomial Optimization, Moments, and Applications
    Springer 2023
  • Gunnar Fløystad, Cordian Riener, Satoshi Murai, Kohji Yanagawa :
    MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties
  • Hugues Verdure, Philippe Moustrou, Cordian Riener, Helen Naumann, Thorsten Theobald :
    Symmetries in AM/GM-based optimization
  • Cordian Riener, Saugata Basu, Marie Françoise Roy :
    Foreword to the Special Issue dedicated to the Arctic Applied Algebra conference 2019 in Tromsø
    Journal of Pure and Applied Algebra 2020 DOI
  • Cordian Riener, Ragni Piene :
    Ragni Piene
  • Cordian Riener :
    Symmetries in algorithmic questions in real algebraic geometry
  • Cordian Riener :
    Efficiently computing Betti numbers of symmetric semi algebraic sets
  • Cordian Riener :
    Vandermonde varieties, mirror spaces, and the cohomology of symmetric semi-algebraic sets
  • Cordian Riener :
    Geometry of quadrature rules
  • Cordian Riener :
    Stand på forskningstorg (Matematiske spill og gåter) under Utforsk UiT, Forskningsdagene 2019
  • Cordian Riener :
    Algorithms to compute topological invariants of symmetric semi algebraic sets
  • Cordian Riener :
    Computing the homology of symmetric semi-algebraic sets
  • Cordian Riener :
    Semidefinite optimization and arithmetic progressions
  • Cordian Riener :
    Efficiently computing the Betti numbers of symmetric semi-algebraic sets
  • Cordian Riener, Mohab Safey el Din :
    Real Root Finding for Equivariant Semi-algebraic Systems

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    Real Algebraic Geometry, Optimization, Computational Algebra, Computational Complexity Theory



    2000 - 2006 Mathematical economy (Universität Ulm)
    2003 - 2007 Philosophy (Universität Ulm)
    2004 - 2005 Master 2 Mathematiques (Université de Bordeaux 1)
    2007 - 2011 Dr phil nat in Mathematics (Goethe Universität Frankfurt)
    2009 - 2014 Magister Artium in Philosophy (Goethe Universität Frankfurt
    2018 Habilitation in Mathematics (Universität Konstanz)


    Since 2018:  Associate Professor, UiT, Tromsø.
    2016 - 2018: Acting Professor (W2), Universität Konstanz
    2012 - 2016: Aalto Science Institute Fellow, Aalto Ylliopisto, Helsinki.
    2011 - 2012: Associate Fellow,  Zukunftskolleg,  Konstanz.
    2007- 2011: Research Assistant, Goethe Universität Frankfurt.