Biography

I am a professor of mathematics at UiT The Arctic University of Norway. I am currently also acting as Pro Dean for PhD education at the Faculty of Science and Technology. 

My research interests include real algebraic geometry, optimization, computational complexity, and computer algebra. 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. 

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Interests
  • Computational Complexity
  • Real algebraic Geometry
  • Symmetries in Computations
Education
  • Habilitation in Mathematics, 2018

    University of Konstanz

  • Magister Artium (Philosophy), 2013

    Goethe University Frankfurt

  • PhD in Mathematics, 2011

    Goethe University Frankfurt

  • Dipl. Math. oec., 2006

    Ulm University

  • Master Mathematics, 2005

    Université de Bordeaux

Experience

 
 
 
 
 
UiT The Arctic University of Norway
Professor
UiT The Arctic University of Norway
Apr 2018 – Present Tromsø, Norway
 
 
 
 
 
University of Konstanz
Vertretungsprofessur
University of Konstanz
Oct 2016 – Mar 2018 Konstanz, Germany
 
 
 
 
 
Aalto University
Aalto Science Fellow
Aalto University
Oct 2012 – Feb 2016 Helsinki, Finland
 
 
 
 
 
University of Konstanz
Postdoctoral fellow
University of Konstanz
Apr 2011 – Sep 2012 Konstanz, Germany
 
 
 
 
 
Goethe University
Research Assistant
Goethe University
Jan 2007 – Mar 2011 Frankfurt, Germany

Publications

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(2022). The poset of Specht ideals for hyperoctahedral groups. Arxiv.

DOI

(2022). Equivariant algebraic and semi-algebraic geometry of infinite affine space. arXiv:2203.11921.

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(2022). Polynomial description for the T-Orbit Spaces of Multiplicative Actions. arxiv:2203.13152.

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(2021). Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations. Journal of Symbolic Computation.

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(2021). Return of the plane evolute. arXiv:2110.11691.

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(2021). # P-hardness proofs of matrix immanants evaluated on restricted matrices. arXiv preprint arXiv:2103.04934.

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(2021). Symmetric nonnegative forms and sums of squares. Discrete & Computational Geometry.

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(2021). Symmetry reduction in AM/GM-based optimization. SIAM J. Optimization.

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(2021). Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets. Foundations of Computational Mathematics.

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(2020). Generalized eigenvalue methods for Gaussian quadrature rules. Annales Henri Lebesgue.

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(2020). Reflection groups and cones of sums of squares. arXiv preprint arXiv:2011.09997.

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(2018). Reflection groups, reflection arrangements, and invariant real varieties. Proceedings of the AMS.

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(2018). Real root finding for equivariant semi-algebraic systems. International Symposium on Symbolic and Algebraic Computation.

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(2017). Bounding the equivariant Betti numbers of symmetric semi-algebraic sets. Advances in Mathematics.

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(2017). Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets. Ordered Algebraic Structures and Related Topics, Contemporary Mathematics.

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(2017). On irreducible components of real exponential hypersurfaces. Arnold Mathematical Journal.

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(2016). Deciding positivity of multisymmetric polynomials. Journal of Symbolic Computation.

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(2016). Symmetric semi-algebraic sets and non-negativity of symmetric polynomials. Journal of Pure and Applied Algebra.

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(2013). Exploiting symmetries in SDP-relaxations for polynomial optimization. Mathematics of Operations Research.

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(2012). A note on extrema of linear combinations of elementary symmetric functions. Linear and Multilinear Algebra.

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(2012). On the degree and half-degree principle for symmetric polynomials. Journal of Pure and Applied Algebra.

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(2008). Positive Polynome und semidefinite Optimierung. Jahresbericht der DMV.

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(2006). On extreme forms in dimension 8. Journal de théorie des nombres de Bordeaux.

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Contact

  • cordian.riener@uit.no
  • +47 77 64 40 90
  • Forskningsparken, Tromsø, 9037
  • Forskningsparken 1 4th floor B425
  • DM Me
  • Skype Me