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.
Research interests
Real Algebraic Geometry, Optimization, Computational Algebra, Computational Complexity Theory
Teaching
Member of research group
CV
Education
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2000 - 2006 Mathematical economy (Universität Ulm)
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2003 - 2007 Philosophy (Universität Ulm)
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2004 - 2005 Master 2 Mathematiques (Université de Bordeaux 1)
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2007 - 2011 Dr phil nat in Mathematics (Goethe Universität Frankfurt)
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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