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  3. Cordian Riener
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Institutt for matematikk og statistikk cordian.riener@uit.no +4777644090 Tromsø Forskningsparken 1 B425

Cordian Riener

Prodekan forskningsutdanning, professor i rein matematikk

Stillingsbeskrivelse

 

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.

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.
  • 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.
  • 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.
  • 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.
  • 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. 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.
  • 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. 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; Piene, Ragni. Ragni Piene. 2020 ISBN 978-3-9814032-7-5.s 122 - 129.
  • 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. 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.
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    Forskningsinteresser

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

    Forskerprofil i Cristin
    ResearchGate
    ORCID: https://orcid.org/0000-0002-1192-3500

    Medlem i forskningsgruppe

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

    CV

    • Siden 2019: Professor i Matematikk, UiT, Tromsø.
    • 2018 - 2019: Førsteamanuensis, UiT, Tromsø.
    • 2016 - 2018: fungerende professor (W2), University Const
    • 2012 - 2016: Aalto Science Institute Fellow, Aalto Ylliopisto, Helsingfors.
    • 2011 - 2012: Associate Fellow, Future College, Const.
    • 2007 - 2011: Stipendiat, Goethe Universität Frankfurt.

     

    Utdanning

    • 2000 - 2006 Matematisk økonomi (Universität Ulm)
    • 2003 - 2007 Filosofi Bachelor (Universität Ulm)
    • 2004 - 2005 Master i matematikk (Université de Bordeaux 1)
    • 2007 - 2011 Dr. phil nat i matematikk (Goethe Universität Frankfurt)
    • 2009 - 2014 Magister Artiumi Filosofi (Goethe Universität Frankfurt)
    • 2018             Habilitation in matematikk (University of Konstanz)
    Forskningsparken 1 B425