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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

Mitt vitenskapelige arbeid ligger i samspillet mellom matematikk og teoretisk informatikk. Et fokus i min forskning er på spørsmål knyttet til beregningsmessig kompleksitet av algoritmiske spørsmål i ekte algebraisk geometri og optimalisering. Konkret er jeg interessert i polynomoptimalisering, representasjon av positive polynomer ved summen av kvadrater, momentproblemer, kvadraturformler, algoritmisk kompleksitet, konvekse sett og semibestemt relaksasjon.


Se også min hjemmeside for mer informasjon om forskning og forhåndstrykk.

Jeg leder Algebra-gruppen og er også en av initiativtakerne til Lie-Størmer senter for grunnleggende strukturer i beregnings- og ren matematikk. Jeg fungerer for tiden også som prodekan ved fakultetet for naturvitenskap og teknologi med fokus på PhD-programmet

 

 


  • Hugues Verdure, Philippe Moustrou, Helen Naumann, Cordian Riener, Thorsten Theobald :
    Symmetry Reduction in AM/GM-Based Optimization
    SIAM Journal on Optimization 2022 DOI
  • Philippe Moustrou, Cordian Riener, Hugues Verdure :
    Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations
    Journal of symbolic computation 2021 ARKIV / DOI
  • Saugata Basu, Cordian Riener :
    Vandermonde Varieties, Mirrored Spaces, and the Cohomology of Symmetric Semi-algebraic Sets
    Foundations of Computational Mathematics 2021 DOI
  • Ragni Piene, Cordian Riener, Boris Shapiro :
    Return of the evolute
    arXiv.org 2021 FULLTEKST
  • Grigoriy Blekherman, Cordian Riener :
    Symmetric Non-Negative Forms and Sums of Squares
    Discrete & Computational Geometry 2020 ARKIV / FULLTEKST / DOI
  • Grigoriy Blekherman, Mario Kummer, Cordian Riener, Markus Schweighofer, Cynthia Vinzant :
    Generalized eigenvalue methods for Gaussian quadrature rules
    Annales Henri Lebesgue (AHL) 2020 ARKIV / DOI
  • Saugata Basu, Cordian Riener :
    On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
    Selecta Mathematica, New Series 2018 ARKIV / DOI
  • Tobias Friedl, Cordian Riener, Raman Sanyal :
    Reflection groups, arrangements, and invariant real varieties
    Proceedings of the American Mathematical Society 2018 ARKIV / DOI
  • Saugata Basu, Cordian Riener :
    On the Isotypic Decomposition of Cohomology Modules of Symmetric Semi-algebraic Sets: Polynomial Bounds on Multiplicities
    International mathematics research notices 2018 ARKIV / DOI
  • Cordian Riener, Markus Schweighofer :
    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 DOI
  • Cordian Riener, Nicolai Vorobjov :
    On Irreducible Components of Real Exponential Hypersurfaces
    Arnold Mathematical Journal 2017 DOI
  • Saugata Basu, Cordian Riener :
    Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets
    Contemporary Mathematics 2017 DOI
  • Saugata Basu, Cordian Riener :
    Bounding the equivariant Betti numbers of symmetric semi-algebraic sets
    Advances in Mathematics 2017 DOI
  • Cordian Riener, Paul Görlach, Tillmann Weißer :
    Deciding positivity of multisymmetric polynomials
    Journal of symbolic computation 2016 DOI
  • Cordian Riener :
    Symmetric semi-algebraic sets and non-negativity of symmetric polynomials polynomials
    Journal of Pure and Applied Algebra 2016 DOI
  • Cordian Riener, Thorsten Theobald, Jean Bernard Lasserre, Lina Jansson Andrén :
    Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization
    Mathematics of Operations Research 2013 DOI
  • Cordian Riener, Kovacec Alexander, Kuhlmann Salma :
    A Note on Extrema of Linear Combinations of Elementary Symmetric Functions
    Linear and multilinear algebra 2012
  • Cordian Riener :
    On the degree and half-degree principle for symmetric polynomials
    Journal of Pure and Applied Algebra 2012 DOI
  • Cordian Riener, Thorsten Theobald :
    Positive Polynome und semidefinite Optimierung
    Jahresbericht der Deutschen Mathematiker-Vereinigung (Teubner) 2008
  • Cordian Riener :
    On extreme forms in dimension 8
    Journal de Théorie des Nombres de Bordeaux 2006
  • Hugues Verdure, Philippe Moustrou, Cordian Riener, Helen Naumann, Thorsten Theobald :
    Symmetries in AM/GM-based optimization
    2021
  • Cordian Riener :
    Efficiently computing Betti numbers of symmetric semi algebraic sets
    2020
  • Cordian Riener, Saugata Basu, Marie Françoise Roy :
    Foreword to the Special Issue dedicated to the Arctic Applied Algebra conference 2019 in Tromsø
    Journal of Pure and Applied Algebra 2020 DOI
  • Cordian Riener :
    Symmetries in algorithmic questions in real algebraic geometry
    2020
  • Cordian Riener, Ragni Piene :
    Ragni Piene
    2020
  • Cordian Riener :
    Vandermonde varieties, mirror spaces, and the cohomology of symmetric semi-algebraic sets
    2019
  • Cordian Riener :
    Algorithms to compute topological invariants of symmetric semi algebraic sets
    2019
  • Cordian Riener :
    Geometry of quadrature rules
    2019
  • Cordian Riener :
    Stand på forskningstorg (Matematiske spill og gåter) under Utforsk UiT, Forskningsdagene 2019
    2019
  • Cordian Riener :
    Computing the homology of symmetric semi-algebraic sets
    2018
  • Cordian Riener :
    Efficiently computing the Betti numbers of symmetric semi-algebraic sets
    2018
  • Cordian Riener, Mohab Safey el Din :
    Real Root Finding for Equivariant Semi-algebraic Systems
    2018 FULLTEKST
  • Cordian Riener :
    Semidefinite optimization and arithmetic progressions
    2018

  • De 50 siste resultatene fra Cristin vises på siden. Se alle arbeider i Cristin her →


    Forskningsinteresser

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



    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