Personkort bilde

Cordian Riener

Professor i rein matematikk Institutt for matematikk og statistikk
Engelsk flaggikon Samisk flaggikon

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

  • 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)

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. One of my reserach focuses is on Symmetry in Quantitative and Algorithmic Real Algebraic Geometry. In case you are interested to write a Master thesis in the Algebra group, feel free to contact me. Also note that there is currently to possibility for a PhD position in Tromsø within the POEMA reserach project. I am also very much interested in philosophical questions related to mathematics and in particular determinism.

  • Blekherman, Grigoriy; Riener, Cordian. Symmetric Non-Negative Forms and Sums of Squares. (fulltekst) Discrete & Computational Geometry 2020. ISSN 0179-5376.s doi: https://doi.org/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.

  • 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. 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.

  • 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; 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. 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; 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: https://doi.org/10.1287/moor.1120.0558.

  • 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; 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; 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.

  • Riener, Cordian. Geometry of quadrature rules. Métodos Efectivos en Geometría Algebraica Real 2019-06-21 - 2019-06-22 2019.

  • 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; 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.

  • Riener, Cordian. Geometry of quadrature rules. Métodos Efectivos en Geometría Algebraica Real 2019-06-21 - 2019-06-22 2019.

  • 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; 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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