Bilde av Riener, Cordian
Bilde av Riener, Cordian
Department of Mathematics and Statistics +4777644090

Cordian Riener

Pro-Dean, Professor in mathematics

Job description

I work in the interplay of mathematics and theoretical computer science. One focus of my reserach is on questions releated to computational complexity of algorithmical questions in real algebraic geometry and  optimization. Concretely, 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.

Please visit my Research Homepage for more details on reserach and preprints.

I am leading the Algebra group and I am also one of the initiators of the Lie-Størmer Center for Fundamental Structures in Computational and Pure Mathematics. I currently also serve as pro-dean at the faculty of science and technology with a focus on the PhD program.






  • 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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    Research interests

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


    Teaching History



    • 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 2019:  Professor, UiT, Tromsø.
    • 2018 - 2019 Associate Professir, 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.