Cordian Riener
Job description
I work in the interplay of mathematics and theoretical computer science. One focus of my research is on questions related to the computational complexity of algorithmic questions in real algebraic geometry and optimization. Concretely, I am interested in polynomial optimization, the representation of positive polynomials by sums of squares, moment problems, quadrature formulas, algorithmic complexity, convex sets, and semidefinite relaxation.
Please visit my Research Homepage for more details on research and preprints.
I am leading the Algebra group and I am also one of the initiators of the Lie-Størmer Center for Fundamental Structures in Computational and Pure Mathematics. I currently also serve as a pro-dean at the faculty of science and technology with a focus on the PhD program. I am chair of the Norwegian Mathematics Council and a member of the board of the Abel Prize.
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
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
Sebastian Debus,
Charu Goel,
Salma Kuhlmann,
Cordian Benedikt Riener
:
On nonnegative invariant quartics in type A
Evelyne Hubert,
Tobias Metzlaff,
Philippe Moustrou,
Cordian Benedikt Riener
:
Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
Sebastian Debus,
Cordian Riener
:
Reflection groups and cones of sums of squares
Gabriella Óturai,
Cordian Riener,
Sarah Martiny
:
Attitudes towards mathematics, achievement, and drop-out intentions among STEM and Non-STEM students in Norway
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
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
Philippe Moustrou,
Cordian Benedikt Riener,
Hugues Verdure
:
Symmetries in Polynomial Optimization
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,
Cordian Riener
:
Symmetric Non-Negative Forms and Sums of Squares
Grigoriy Blekherman,
Mario Kummer,
Cordian Riener,
Markus Schweighofer,
Cynthia Vinzant
:
Generalized eigenvalue methods for Gaussian quadrature rules
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
Saugata Basu,
Cordian Riener
:
On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms
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
:
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
The 50 latest publications is shown on this page. See all publications in Cristin here →
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 economics (Universität Ulm)
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2003 - 2007 Philosophy (Universität Ulm)
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2004 - 2005 Master 2 Mathematiques pures (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 Professor, 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.
Service
- 2023 - Norwegian Mathematics Council (chair)
- 2022 - Steering Board of the Abel Prize
- 2022 - 2023 SIAM AG Algebraic Geometry (officer)
- 2019 - 2020 Faculty board (NT Faculty UiT)
Conference organization
- ISSAC 2023 (Tromsø - chair local organization)
- Nasjonalt Matematikermøte 2022 (Tromsø - local organization committee)
- Baltic Way 2022 (Tromsø - chair local organization committee)
- Nordic Combinatorial Conference 2022 (Tromsø - local organization committee)
- Lie-Størmer Colloquium 2020 (Rosendal - organization committee)
- MEGA 2021 (Tromsø - virtual- chair local organization)
- A^3 — Arctic Applied Algebra (Tromsø - chair local organization committee)
- Applications of Real Algebraic Geometry 2014 (Aalto University)
- Mathematics, Algorithms, and Proofs 2012 (organizational committee)
Organization of smaller mathematical gatherings
- Combinatorial Hopf algebras and modern Lie theory with applications (Summer school Nordfjordeid)
- Symmetry, Stability, and Interactions with Computation (CIRM 2023)
- CATMI (Bergen -scientific committee)
- Topics in real and tropical algebraic geometry (Summer school Nordfjordeid)
- MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (MFO)
- Summer school in Algebraic Statistics (2018 UiT)