Cordian Riener
Prodekan forskningsutdanning, professor i 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
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
Ragni Piene,
Cordian Riener,
Boris Shapiro
:
Return of the evolute
Gabriella Óturai,
Cordian Riener,
Sarah Martiny
:
Attitudes towards mathematics, achievement, and drop-out intentions among STEM and Non-STEM students in Norway
Cordian Riener,
Sebastian Debus
:
Reflection groups and cones of sums of squares
Cordian Benedikt Riener,
Robin Leonid Schabert
:
Linear slices of Hyperbolic polynomials and positivity of symmetric polynomial functions
Sebastian Debus,
Philippe Moustrou,
Cordian Benedikt Riener,
Hugues Verdure
:
The poset of Specht ideals for hyperoctahedral groups
Algebraic combinatorics 2023 ARKIV
Philippe Moustrou,
Helen Naumann,
Cordian Riener,
Thorsten Theobald,
Hugues Verdure
:
Symmetry Reduction in AM/GM-Based Optimization
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
Grigoriy Blekherman,
Mario Kummer,
Cordian Riener,
Markus Schweighofer,
Cynthia Vinzant
:
Generalized eigenvalue methods for Gaussian quadrature rules
Grigoriy Blekherman,
Cordian Riener
:
Symmetric Non-Negative Forms and Sums of Squares
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
Saugata Basu,
Cordian Riener
:
On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
Tobias Friedl,
Cordian Riener,
Raman Sanyal
:
Reflection groups, arrangements, and invariant real varieties
Saugata Basu,
Cordian Riener
:
On the Isotypic Decomposition of Cohomology Modules of Symmetric Semi-algebraic Sets: Polynomial Bounds on Multiplicities
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
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
:
Efficiently computing Betti numbers of symmetric semi algebraic sets
2020
Cordian Riener
:
Symmetries in algorithmic questions in real algebraic geometry
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
:
Vandermonde varieties, mirror spaces, and the cohomology of symmetric semi-algebraic sets
2019
Cordian Riener
:
Geometry of quadrature rules
2019
Cordian Riener
:
Algorithms to compute topological invariants of symmetric semi algebraic sets
2019
Cordian Riener
:
Stand på forskningstorg (Matematiske spill og gåter) under Utforsk UiT, Forskningsdagene 2019
2019
Cordian Riener,
Mohab Safey el Din
:
Real Root Finding for Equivariant Semi-algebraic Systems
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
:
Semidefinite optimization and arithmetic progressions
2018
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Forskningsinteresser
Real Algebraic Geometry, Optimization, Computational Algebra, Computational Complexity Theory
Medlem i forskningsgruppe
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)