Bilde av Riener, Cordian
Bilde av Riener, Cordian
Prodekan forskningsutdanning, professor i matematikk Institutt for matematikk og statistikk cordian.riener@uit.no +4777644090

Cordian Riener


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

 

 


  • Cordian Benedikt Riener, Robin Leonid Schabert, Thi Xuan Vu :
    Connectivity in Symmetric Semi-Algebraic Sets
    Association for Computing Machinery 2024 DOI
  • Ragni Piene, Cordian Riener, Boris Shapiro :
    Return of the evolute
    Annales de l'Institut Fourier 2024 FULLTEKST / ARKIV
  • Philippe Moustrou, Cordian Benedikt Riener, Thorsten Theobald, Hugues Verdure :
    Symmetric SAGE and SONC forms, exactness and quantitative gaps
    Journal of symbolic computation 2024 DOI
  • Evelyne Hubert, Tobias Metzlaff, Cordian Benedikt Riener :
    Orbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description
    SIAM Journal on applied algebra and geometry 2024 ARKIV / DOI
  • Sebastian Debus, Charu Goel, Salma Kuhlmann, Cordian Benedikt Riener :
    On nonnegative invariant quartics in type A
    Journal of symbolic computation 2024 ARKIV / DOI
  • Evelyne Hubert, Tobias Metzlaff, Philippe Moustrou, Cordian Benedikt Riener :
    Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
    Mathematical programming 2024 DOI
  • Cordian Benedikt Riener, Robin Leonid Schabert :
    Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions
    Journal of Pure and Applied Algebra 2023 ARKIV / DOI
  • Sebastian Debus, Philippe Moustrou, Cordian Benedikt Riener, Hugues Verdure :
    The poset of Specht ideals for hyperoctahedral groups
    Algebraic combinatorics 2023 ARKIV / DOI
  • Thi Xuan Vu, Mohab Safey el Din, George Labahn, Cordian Benedikt Riener, Éric Schost :
    Faster real root decision algorithm for symmetric polynomials
    Association for Computing Machinery 2023 DOI
  • Sebastian Debus, Cordian Riener :
    Reflection groups and cones of sums of squares
    Journal of symbolic computation 2023 ARKIV / DOI
  • Gabriella Óturai, Cordian Riener, Sarah Martiny :
    Attitudes towards mathematics, achievement, and drop-out intentions among STEM and Non-STEM students in Norway
    International Journal of Educational Research Open 2023 ARKIV / DOI
  • Philippe Moustrou, Cordian Benedikt Riener, Hugues Verdure :
    Symmetries in Polynomial Optimization
    Springer 2023 ARKIV / DOI
  • Philippe Moustrou, Helen Naumann, Cordian Riener, Thorsten Theobald, Hugues Verdure :
    Symmetry Reduction in AM/GM-Based Optimization
    SIAM Journal on Optimization 2022 ARKIV / DOI
  • Saugata Basu, Cordian Riener :
    Vandermonde Varieties, Mirrored Spaces, and the Cohomology of Symmetric Semi-algebraic Sets
    Foundations of Computational Mathematics 2021 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
  • 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
  • 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
  • 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 equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
    Selecta Mathematica, New Series 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 (IMRN) 2018 ARKIV / 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 :
    Symmetric semi-algebraic sets and non-negativity of symmetric polynomials polynomials
    Journal of Pure and Applied Algebra 2016 DOI
  • Cordian Riener, Paul Görlach, Tillmann Weißer :
    Deciding positivity of multisymmetric polynomials
    Journal of symbolic computation 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
  • Michal Kočvara, Bernard Mourrain, Cordian Benedikt Riener :
    Polynomial Optimization, Moments, and Applications
    Springer 2023
  • Petter Bjørklund, Elisabeth Wetzer, Cordian Benedikt Riener :
    Feirer Kvinner i matematikk-dagen på Verdensteatret
    uit.no 2024
  • Gabriella Oturai, Sarah Elisabeth Martiny, Johanne Sofie Dalvik, Cordian Benedikt Riener :
    Norwegian students' views on mathematics and mathematicians
    2024
  • Gunnar Fløystad, Cordian Riener, Satoshi Murai, Kohji Yanagawa :
    MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties
    2022
  • Hugues Verdure, Philippe Moustrou, Cordian Riener, Helen Naumann, Thorsten Theobald :
    Symmetries in AM/GM-based optimization
    2021
  • Cordian Riener, Ragni Piene :
    Ragni Piene
    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 :
    Efficiently computing Betti numbers of symmetric semi algebraic sets
    2020
  • Cordian Riener :
    Stand på forskningstorg (Matematiske spill og gåter) under Utforsk UiT, Forskningsdagene 2019
    2019
  • Cordian Riener :
    Algorithms to compute topological invariants of symmetric semi algebraic sets
    2019
  • Cordian Riener :
    Geometry of quadrature rules
    2019
  • Cordian Riener :
    Vandermonde varieties, mirror spaces, and the cohomology of symmetric semi-algebraic sets
    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
  • 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, Zukunftskolleg, Konstanz.
    • 2007 - 2011: Stipendiat, Goethe Universität Frankfurt.

     

    Utdanning

    2000 - 2006 Matematisk økonomi (Universität Ulm)
    2003 - 2007 Filosofi (Universität Ulm)
    2004 - 2005 Master 2 i rene matematikk (Université de Bordeaux 1)
    2007 - 2011 Dr. Phil nat i matematikk (Goethe Universität Frankfurt)
    2009 - 2014 Magister Artium i filosofi (Goethe Universität Frankfurt)
    2018 Habilitering i matematikk (Universität Konstanz)
    Stilling

    Siden 2019: Professor, UiT, Tromsø.
    2018 - 2019 Førsteamanuensis, UiT, Tromsø.
    2016 - 2018: Vikarierende professor (W2), Universität Konstanz.
    2012 - 2016: Aalto Science Institute Fellow, Aalto Ylliopisto, Helsingfors.
    2011 - 2012: Associate Fellow, Zukunftskolleg, Konstanz.
    2007 - 2011: Forskningsassistent, Goethe Universität Frankfurt.
    Tjeneste

    2023 - Norsk matematikkråd (leder)
    2022 - Styret for Abelprisen
    2022 - 2023 SIAM AG Algebraisk Geometri (offiser)
    2019 - 2020 Fakultetsstyret (NT Fakultet UiT)
    Konferanseorganisasjon

    ISSAC 2023 (Tromsø - leder av lokal organisasjon)
    Nasjonalt Matematikermøte 2022 (Tromsø - lokal organisasjonskomité)
    Baltic Way 2022 (Tromsø - leder av lokal organisasjonskomité)
    Nordisk Kombinatorisk Konferanse 2022 (Tromsø - lokal organisasjonskomité)
    Lie-Størmer Kolloquium 2020 (Rosendal - organisasjonskomité)
    MEGA 2021 (Tromsø - virtuelt - leder av lokal organisasjon)
    A^3 — Arctic Applied Algebra (Tromsø - leder av lokal organisasjonskomité)
    Applications of Real Algebraic Geometry 2014 (Aalto Universitet)
    Mathematics, Algorithms, and Proofs 2012 (organisasjonskomité)
    Organisering av mindre matematiske samlinger

    Kombinatoriske Hopf-algebraer og moderne Lie-teori med anvendelser (Sommerskole Nordfjordeid)
    Symmetri, stabilitet og interaksjoner med beregning (CIRM 2023)
    CATMI (Bergen - vitenskapelig komité)
    Temaer i reell og tropisk algebraisk geometri (Sommerskole Nordfjordeid)
    MFO-RIMS Tandem Workshop: Symmetrier på polynomidealer og varianter (MFO)
    Sommerskole i Algebraisk Statistikk (2018 UiT)