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Department of Mathematics and Statistics cordian.riener@uit.no +4777644090 Tromsø Forskningsparken 1 B425

Cordian Riener

Pro-Dean, Professor in mathematics

Job description

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.

 

 

  • Verdure, Hugues; Moustrou, Philippe; Naumann, Helen; Riener, Cordian; Theobald, Thorsten. Symmetry Reduction in AM/GM-Based Optimization. SIAM Journal on Optimization 2022; Volum 32 (2). ISSN 1052-6234.s 765 - 785.s doi: 10.1137/21M1405691.
  • Piene, Ragni; Riener, Cordian; Shapiro, Boris. Return of the evolute. (fulltekst) arXiv.org 2021. ISSN 2331-8422.
  • Basu, Saugata; Riener, Cordian. Vandermonde Varieties, Mirrored Spaces, and the Cohomology of Symmetric Semi-algebraic Sets. Foundations of Computational Mathematics 2021. ISSN 1615-3375.s doi: 10.1007/s10208-021-09519-7.
  • Moustrou, Philippe; Riener, Cordian; Verdure, Hugues. Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations. Journal of symbolic computation 2021; Volum 107. ISSN 0747-7171.s 106 - 121.s doi: 10.1016/j.jsc.2021.02.002.
  • Blekherman, Grigoriy; Kummer, Mario; Riener, Cordian; Schweighofer, Markus; Vinzant, Cynthia. Generalized eigenvalue methods for Gaussian quadrature rules. Annales Henri Lebesgue (AHL) 2020; Volum 3.s 1327 - 1341.s doi: 10.5802/ahl.62.
  • Blekherman, Grigoriy; Riener, Cordian. Symmetric Non-Negative Forms and Sums of Squares. (fulltekst) Discrete & Computational Geometry 2020; Volum 65. ISSN 0179-5376.s 764 - 799.s doi: 10.1007/s00454-020-00208-w.
  • Riener, Cordian; Schweighofer, Markus. 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; Volum 45. ISSN 0885-064X.s 22 - 54.s doi: 10.1016/j.jco.2017.10.002.
  • Friedl, Tobias; Riener, Cordian; Sanyal, Raman. Reflection groups, arrangements, and invariant real varieties. Proceedings of the American Mathematical Society 2018; Volum 146 (3). ISSN 0002-9939.s 1031 - 1045.s doi: 10.1090/proc/13821.
  • Basu, Saugata; Riener, Cordian. On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms. Selecta Mathematica, New Series 2018; Volum 24 (4). ISSN 1022-1824.s 3241 - 3281.s doi: 10.1007/s00029-018-0401-7.
  • Basu, Saugata; Riener, Cordian. On the Isotypic Decomposition of Cohomology Modules of Symmetric Semi-algebraic Sets: Polynomial Bounds on Multiplicities. International mathematics research notices 2018; Volum 2020 (7). ISSN 1073-7928.s 2054 - 2113.s doi: 10.1093/imrn/rny062.
  • Basu, Saugata; Riener, Cordian. Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets. Contemporary Mathematics 2017; Volum 697. ISSN 0271-4132.s 53 - 81.s doi: 10.1090/conm/697/14046.
  • Riener, Cordian; Vorobjov, Nicolai. On Irreducible Components of Real Exponential Hypersurfaces. Arnold Mathematical Journal 2017; Volum 3 (3). ISSN 2199-6792.s 423 - 443.s doi: 10.1007/s40598-017-0073-y.
  • Basu, Saugata; Riener, Cordian. Bounding the equivariant Betti numbers of symmetric semi-algebraic sets. Advances in Mathematics 2017; Volum 305. ISSN 0001-8708.s 803 - 855.s doi: 10.1016/j.aim.2016.09.015.
  • Riener, Cordian. Symmetric semi-algebraic sets and non-negativity of symmetric polynomials polynomials. Journal of Pure and Applied Algebra 2016; Volum 220 (4). ISSN 0022-4049.s 2809 - 2815.s doi: 10.1016/j.jpaa.2015.12.010.
  • Riener, Cordian; Görlach, Paul; Weißer, Tillmann. Deciding positivity of multisymmetric polynomials. Journal of symbolic computation 2016; Volum 74. ISSN 0747-7171.s 603 - 616.s doi: 10.1016/j.jsc.2015.10.001.
  • Riener, Cordian; Theobald, Thorsten; Lasserre, Jean Bernard; Andrén, Lina Jansson. Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization. Mathematics of Operations Research 2013; Volum 38 (1). ISSN 0364-765X.s 122 - 141.s doi: 10.1287/moor.1120.0558.
  • Riener, Cordian; Alexander, Kovacec; Salma, Kuhlmann. A Note on Extrema of Linear Combinations of Elementary Symmetric Functions. Linear and multilinear algebra 2012; Volum 60 (2). ISSN 0308-1087.s 219 - 224.
  • Riener, Cordian. On the degree and half-degree principle for symmetric polynomials. Journal of Pure and Applied Algebra 2012; Volum 216 (4). ISSN 0022-4049.s 850 - 854.s doi: 10.1016/j.jpaa.2011.08.012.
  • Riener, Cordian; Theobald, Thorsten. Positive Polynome und semidefinite Optimierung. Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner) 2008; Volum 110 (2). ISSN 0012-0456.s 57 - 74.
  • Riener, Cordian. On extreme forms in dimension 8. Journal de Théorie des Nombres de Bordeaux 2006; Volum 18 (3). ISSN 1246-7405.s 677 - 682.
  • Verdure, Hugues; Moustrou, Philippe; Riener, Cordian; Naumann, Helen; Theobald, Thorsten. Symmetries in AM/GM-based optimization. SIAM Conference on Applied Algebraic Geometry (AG21) 2021-08-16 - 2021-08-20 2021.
  • Riener, Cordian; Basu, Saugata; Roy, Marie Françoise. Foreword to the Special Issue dedicated to the Arctic Applied Algebra conference 2019 in Tromsø. Journal of Pure and Applied Algebra 2020. ISSN 0022-4049.s doi: 10.1016/j.jpaa.2020.106639.
  • Riener, Cordian; Piene, Ragni. Ragni Piene. 2020 ISBN 978-3-9814032-7-5.s 122 - 129.
  • Riener, Cordian. Efficiently computing Betti numbers of symmetric semi algebraic sets. DMV Annual Meeting 2020 2020-09-14 - 2020-09-18 2020.
  • Riener, Cordian. Symmetries in algorithmic questions in real algebraic geometry. POEMA Online Learning Weeks 2020-07-08 - 2020-07-22 2020.
  • Riener, Cordian. Stand på forskningstorg (Matematiske spill og gåter) under Utforsk UiT, Forskningsdagene 2019. Utforsk UiT 19. september, Forskningsdagene 2019 2019-09-19 - 2019-09-19 2019.
  • Riener, Cordian. Algorithms to compute topological invariants of symmetric semi algebraic sets. Geometry of Real Polynomials, Convexity and Optimization 2019-05-26 - 2019-05-31 2019.
  • Riener, Cordian. Vandermonde varieties, mirror spaces, and the cohomology of symmetric semi-algebraic sets. Effective Methods in Algebraic Geometry 2019-06-17 - 2019-06-21 2019.
  • Riener, Cordian. Geometry of quadrature rules. Métodos Efectivos en Geometría Algebraica Real 2019-06-21 - 2019-06-22 2019.
  • Riener, Cordian; Safey el Din, Mohab. Real Root Finding for Equivariant Semi-algebraic Systems. International Symposium on Symbolic and Algebraic Computation 2018 (fulltekst) 2018-07-16 - 2018-07-19 2018.
  • Riener, Cordian. Semidefinite optimization and arithmetic progressions. International Symposium on Mathematical Programming (ISMP) 2018-07-01 - 2018-07-06 2018.
  • Riener, Cordian. Efficiently computing the Betti numbers of symmetric semi-algebraic sets. Séminaire de géométrie et singularités 2018-07-09 - 2018-07-09 2018.
  • Riener, Cordian. Computing the homology of symmetric semi-algebraic sets. Symmetry and Computation - Symétries dans les méthodes de calcul 2018-04-03 - 2018-04-07 2018.
    • Look at all works in CRIStin →

    Research interests

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

    Teaching

    Teaching History

    Researcher profile in Cristin
    ResearchGate
    ORCID: https://orcid.org/0000-0002-1192-3500

    Member of research group

    Algebra   English content LIE-STØRMER CENTER   English content MASCOT   English content

    CV

    Education

    • 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)

    Positions

    • 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. 

     

    Forskningsparken 1 B425