Bilde av Riener, Cordian
Bilde av Riener, Cordian
Department of Mathematics and Statistics cordian.riener@uit.no +4777644090 Tromsø

Cordian Riener


Job description

Jeg er professor i matematikk og arbeider i skjæringsfeltet mellom matematikk og teoretisk informatikk. Forskningen min handler om reell algebraisk geometri, polynomoptimering og beregningskompleksitet. Et gjennomgående tema er symmetri – hvordan symmetrier, særlig fra endelige refleksjonsgrupper, kan brukes til å forstå geometrien og topologien til reelle algebraiske og semialgebraiske mengder, og til å gjøre algoritmiske problemer i optimering og datamaskinalgebra enklere å løse. Mer om forskningen og preprints finner du på hjemmesiden min.

Ved UiT er jeg prodekan for forskerutdanning ved Fakultet for naturvitenskap og teknologi. Jeg er også medleder for Lie–Størmer-senteret, et nasjonalt senter for grunnleggende strukturer i beregningsorientert og ren matematikk som UiT driver sammen med Universitetet i Bergen, og vitenskapelig koordinator for den nasjonale forskerskolen Mathesis.

Utenfor UiT leder jeg Norsk matematikkråd, sitter i styret for Abelprisen og er Editor-in-Chief for tidsskriftet Journal of Symbolic Computation.


  • Istvan Miklos, Cordian Riener :
    #P-Hardness proofs of matrix immanants evaluated on restricted matrices
    Theoretical Computer Science 04. diciembre 2025 DOI / ARKIV
  • Jose Acevedo, Grigoriy Blekherman, Sebastian Debus, Cordian Riener :
    The Wonderful Geometry of the Vandermonde map
    Foundations of Computational Mathematics 22. septiembre 2025 DOI / ARKIV
  • Sebastian Debus, Cordian Riener, Robin Leonid Schabert :
    Slices of Stable Polynomials and Connections to the Grace-Walsh-Szegő Theorem
    Journal of symbolic computation 2025 DOI / ARKIV
  • Philippe Moustrou, Cordian Riener, Robin Leonid Schabert :
    Constructively describing orbit spaces of finite groups by few inequalities
    Journal of symbolic computation 2025 DOI / ARKIV
  • Cordian Riener, Jan Rolfes, Frank Vallentin :
    A semidefinite programming hierarchy for covering problems in discrete geometry
    Numerical Algebra, Control and Optimization 2025 DOI / ARKIV
  • Ragni Piene, Cordian Riener, Boris Shapiro :
    Return of the plane evolute
    Annales de l'Institut Fourier 2025 DOI / ARKIV / ARKIV / FULLTEKST
  • Jose Acevedo, Grigoriy Blekherman, Sebastian Debus, Cordian Riener :
    Symmetric nonnegative functions, the tropical Vandermonde cell and superdominance of power sums
    Collectanea Mathematica 2025 DOI / ARKIV
  • Mario Kummer, Cordian Benedikt Riener :
    Equivariant algebraic and semi-algebraic geometry of infinite affine space
    Journal of Algebra 2024 DOI / ARKIV
  • Sebastian Debus, Charu Goel, Salma Kuhlmann, Cordian Benedikt Riener :
    On nonnegative invariant quartics in type A
    Journal of symbolic computation 2024 DOI / ARKIV
  • Cordian Benedikt Riener, Robin Leonid Schabert, Thi Xuan Vu :
    Connectivity in Symmetric Semi-Algebraic Sets
    Association for Computing Machinery 2024 DOI / ARKIV
  • Philippe Moustrou, Cordian Benedikt Riener, Thorsten Theobald, Hugues Verdure :
    Symmetric SAGE and SONC forms, exactness and quantitative gaps
    Journal of symbolic computation 2024 DOI / ARKIV
  • Evelyne Hubert, Tobias Metzlaff, Philippe Moustrou, Cordian Benedikt Riener :
    Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
    Mathematical programming 2024 DOI / ARKIV
  • Evelyne Hubert, Tobias Metzlaff, Cordian Benedikt Riener :
    Orbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description
    SIAM Journal on applied algebra and geometry 2024 DOI / ARKIV
  • Philippe Moustrou, Cordian Benedikt Riener, Hugues Verdure :
    Symmetries in Polynomial Optimization
    2023 DOI / 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 DOI / ARKIV
  • Cordian Benedikt Riener, Robin Leonid Schabert :
    Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions
    Journal of Pure and Applied Algebra 2023 DOI / ARKIV
  • Sebastian Debus, Philippe Moustrou, Cordian Benedikt Riener, Hugues Verdure :
    The poset of Specht ideals for hyperoctahedral groups
    Algebraic combinatorics 2023 DOI / ARKIV
  • 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 / ARKIV
  • Sebastian Debus, Cordian Riener :
    Reflection groups and cones of sums of squares
    Journal of symbolic computation 2023 DOI / ARKIV
  • Philippe Moustrou, Helen Naumann, Cordian Riener, Thorsten Theobald, Hugues Verdure :
    Symmetry Reduction in AM/GM-Based Optimization
    SIAM Journal on Optimization 2022 DOI / ARKIV
  • Saugata Basu, Cordian Riener :
    Vandermonde Varieties, Mirrored Spaces, and the Cohomology of Symmetric Semi-algebraic Sets
    Foundations of Computational Mathematics 2021 DOI / ARKIV
  • Philippe Moustrou, Cordian Riener, Hugues Verdure :
    Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations
    Journal of symbolic computation 2021 DOI / ARKIV
  • Grigoriy Blekherman, Cordian Riener :
    Symmetric Non-Negative Forms and Sums of Squares
    Discrete & Computational Geometry 2020 DOI / ARKIV / FULLTEKST
  • Grigoriy Blekherman, Mario Kummer, Cordian Riener, Markus Schweighofer, Cynthia Vinzant :
    Generalized eigenvalue methods for Gaussian quadrature rules
    Annales Henri Lebesgue (AHL) 2020 DOI / ARKIV
  • Tobias Friedl, Cordian Riener, Raman Sanyal :
    Reflection groups, arrangements, and invariant real varieties
    Proceedings of the American Mathematical Society 2018 DOI / ARKIV
  • Saugata Basu, Cordian Riener :
    On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
    Selecta Mathematica, New Series 2018 DOI / ARKIV
  • Michal Kočvara, Bernard Mourrain, Cordian Benedikt Riener :
    Polynomial Optimization, Moments, and Applications
    Springer 2023 DOI / ARKIV
  • Cordian Riener, Kurusch Ebrahimi-Fard, Alexander Schmeding :
    Når friksjonen forsvinner
    25. junio 2026 ARKIV
  • Cordian Riener, Kurusch Ebrahimi-Fard, Alexander Schmeding :
    KI lager matematiske bevis – forskere må kontrollere
    12. agosto 2026 ARKIV
  • Cordian Riener, Hans Zanna Munthe-Kaas :
    Tiden er inne for Matematikkens hus
    2025 ARKIV
  • Helge Holden, Hans Zanna Munthe-Kaas, Dag Rune Olsen, Cordian Benedikt Riener :
    Norge trenger et løft for matematikk på høyt nivå
    Nordnorsk debatt - Nordlys 16. enero 2025 ARKIV
  • Cordian Riener, Hans Munthe-Kaas, Marta Panizzut, Elisabeth Wetzer :
    Women in Mathematics
    2025 ARKIV
  • Cordian Riener :
    The wonderful geometry of the Vandermonde map: Symmetry at infinity and applications
    2025 ARKIV
  • Petter Bjørklund, Elisabeth Wetzer, Cordian Benedikt Riener :
    Feirer Kvinner i matematikk-dagen på Verdensteatret
    uit.no 2024 ARKIV
  • Gabriella Oturai, Cordian Benedikt Riener :
    Disse resultatene i matte og naturfag er et varsko for norsk skole
    Aftenposten 05. diciembre 2024 ARKIV / FULLTEKST
  • Gabriella Oturai, Sarah Elisabeth Martiny, Johanne Sofie Dalvik, Cordian Benedikt Riener :
    Norwegian students' views on mathematics and mathematicians
    2024 ARKIV
  • Gunnar Fløystad, Cordian Riener, Satoshi Murai, Kohji Yanagawa :
    MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties
    Mathematisches Forschungsinstitut Oberwolfach 2022 ARKIV
  • Hugues Verdure, Philippe Moustrou, Cordian Riener, Helen Naumann, Thorsten Theobald :
    Symmetries in AM/GM-based optimization
    2021 ARKIV
  • Cordian Riener, Ragni Piene :
    Ragni Piene
    2020 ARKIV
  • 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 / ARKIV
  • Cordian Riener :
    Symmetries in algorithmic questions in real algebraic geometry
    2020 ARKIV
  • Cordian Riener :
    Efficiently computing Betti numbers of symmetric semi algebraic sets
    2020 ARKIV
  • Cordian Riener :
    Stand på forskningstorg (Matematiske spill og gåter) under Utforsk UiT, Forskningsdagene 2019
    2019 ARKIV
  • Cordian Riener :
    Algorithms to compute topological invariants of symmetric semi algebraic sets
    2019 ARKIV
  • Cordian Riener :
    Geometry of quadrature rules
    2019 ARKIV
  • Cordian Riener :
    Vandermonde varieties, mirror spaces, and the cohomology of symmetric semi-algebraic sets
    2019 ARKIV
  • Cordian Riener :
    Computing the homology of symmetric semi-algebraic sets
    2018 ARKIV
  • Cordian Riener :
    Efficiently computing the Betti numbers of symmetric semi-algebraic sets
    2018 ARKIV
  • Cordian Riener :
    Semidefinite optimization and arithmetic progressions
    2018 ARKIV
  • Cordian Riener, Mohab Safey el Din :
    Real Root Finding for Equivariant Semi-algebraic Systems

  • The 50 latest publications is shown on this page. See all publications in NVA here →


    Research interests

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

    Teaching

    Jeg underviser på alle nivåer, fra grunnkurs til spesialcurriculum for master- og ph.d.-studenter.

    Ordinære emner

    • Reell algebraisk geometri
    • Algebraisk geometri
    • Algebra 1 og Algebra 2
    • Kalkulus 3
    • Lineær algebra (MAT-1004 / MAT-1020)
    • Numeriske metoder

    Spesialpensum (master/ph.d.)

    • Mathematical Optimization: Convexity, Duality, and Convexification
    • Geometric Combinatorics
    • Symmetry in Computation
    • Invariant Theory and Representation Theory
    • Semidefinite Programming and Polynomial Optimization

    Nettbaserte mikroemner

    • MIK-1018 What Is Mathematics?
    • MIK-1019 Making Optimal Decisions



    CV

    Utdanning

    • 2000–2006: Matematisk økonomi (Wirtschaftsmathematik), Universität Ulm
    • 2003–2007: Filosofi, Universität Ulm
    • 2004–2005: Master 2 i ren matematikk, Université de Bordeaux 1
    • 2007–2011: Dr. phil. nat. i matematikk, Goethe-Universität Frankfurt
    • 2009–2014: Magister Artium i filosofi, Goethe-Universität Frankfurt
    • 2018: Habilitasjon i matematikk, Universität Konstanz

    Stillinger

    Verv

    Veiledning

    Ph.d.-kandidater

    • Pågående: Gaël Druez, Henri Breloer, Örs Rekák, Luca Wellmeier
    • 2024: Robin Schabert
    • 2024: Arne Lien
    • 2022: Sebastian Debus
    • 2018: Jan Rolfes

    Postdoktorer

    • Philippe Moustrou, Thi Xuan Vu, Tobias Boege, Ettore Teixeira Turatti, Rodolfo Ríos-Zertuche

    Masterstudenter

    • 2023: Elias Sandal, Alessandro Schena
    • 2022: Ingar Wesenberg Eskeland
    • 2021: Pedro González
    • 2020: Arne Lien

    Konferanseorganisering

    Sommerskoler og workshops