Cordian Riener
Job description
I am a professor of mathematics at UiT, where I lead the Applied and Computational Algebra group. My research lies at the interface of mathematics and theoretical computer science: real algebraic geometry, polynomial optimization, symbolic computation and computational complexity. Running through all of it is symmetry – how the symmetry of a problem can be turned from a feature of the problem into the very thing that makes it solvable. An overview of my research themes and preprints is on my homepage.
At UiT I am Pro-Dean for PhD education at the Faculty of Science and Technology. I also co-direct the Lie–Størmer Centre, a national centre for fundamental structures in computational and pure mathematics run jointly by UiT and the University of Bergen, and I coordinate the national PhD school Mathesis.
Beyond UiT, I chair the Norwegian Mathematics Council, serve on the board of the Abel Prize, and am Editor-in-Chief of the Journal of Symbolic Computation.
See also: Google Scholar · arXiv · dblp
Istvan Miklos,
Cordian Riener
:
#P-Hardness proofs of matrix immanants evaluated on restricted matrices
Jose Acevedo,
Grigoriy Blekherman,
Sebastian Debus,
Cordian Riener
:
The Wonderful Geometry of the Vandermonde map
Sebastian Debus,
Cordian Riener,
Robin Leonid Schabert
:
Slices of Stable Polynomials and Connections to the Grace-Walsh-Szegő Theorem
Philippe Moustrou,
Cordian Riener,
Robin Leonid Schabert
:
Constructively describing orbit spaces of finite groups by few inequalities
Cordian Riener,
Jan Rolfes,
Frank Vallentin
:
A semidefinite programming hierarchy for covering problems in discrete geometry
Ragni Piene,
Cordian Riener,
Boris Shapiro
:
Return of the plane evolute
Jose Acevedo,
Grigoriy Blekherman,
Sebastian Debus,
Cordian Riener
:
Symmetric nonnegative functions, the tropical Vandermonde cell and superdominance of power sums
Mario Kummer,
Cordian Benedikt Riener
:
Equivariant algebraic and semi-algebraic geometry of infinite affine space
Sebastian Debus,
Charu Goel,
Salma Kuhlmann,
Cordian Benedikt Riener
:
On nonnegative invariant quartics in type A
Cordian Benedikt Riener,
Robin Leonid Schabert,
Thi Xuan Vu
:
Connectivity in Symmetric Semi-Algebraic Sets
Philippe Moustrou,
Cordian Benedikt Riener,
Thorsten Theobald,
Hugues Verdure
:
Symmetric SAGE and SONC forms, exactness and quantitative gaps
Evelyne Hubert,
Tobias Metzlaff,
Philippe Moustrou,
Cordian Benedikt Riener
:
Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
Evelyne Hubert,
Tobias Metzlaff,
Cordian Benedikt Riener
:
Orbit Spaces of Weyl Groups Acting on Compact Tori: A Unified and Explicit Polynomial Description
Philippe Moustrou,
Cordian Benedikt Riener,
Hugues Verdure
:
Symmetries in Polynomial Optimization
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
Sebastian Debus,
Cordian Riener
:
Reflection groups and cones of sums of squares
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
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
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
Michal Kočvara,
Bernard Mourrain,
Cordian Benedikt Riener
:
Polynomial Optimization, Moments, and Applications
Cordian Riener,
Kurusch Ebrahimi-Fard,
Alexander Schmeding
:
Når friksjonen forsvinner
25. June 2026 ARKIV
Cordian Riener,
Kurusch Ebrahimi-Fard,
Alexander Schmeding
:
KI lager matematiske bevis – forskere må kontrollere
12. August 2026 ARKIV
Cordian Riener,
Hans Zanna Munthe-Kaas
:
Tiden er inne for Matematikkens hus
2025 ARKIV
Helge Holden,
Hans Zanna Munthe-Kaas,
Dag Rune Olsen,
Cordian Benedikt Riener
:
Norge trenger et løft for matematikk på høyt nivå
Nordnorsk debatt - Nordlys 16. January 2025 ARKIV
Cordian Riener,
Hans Munthe-Kaas,
Marta Panizzut,
Elisabeth Wetzer
:
Women in Mathematics
2025 ARKIV
Cordian Riener
:
The wonderful geometry of the Vandermonde map: Symmetry at infinity and applications
2025 ARKIV
Petter Bjørklund,
Elisabeth Wetzer,
Cordian Benedikt Riener
:
Feirer Kvinner i matematikk-dagen på Verdensteatret
uit.no 2024 ARKIV
Gabriella Oturai,
Cordian Benedikt Riener
:
Disse resultatene i matte og naturfag er et varsko for norsk skole
Gabriella Oturai,
Sarah Elisabeth Martiny,
Johanne Sofie Dalvik,
Cordian Benedikt Riener
:
Norwegian students' views on mathematics and mathematicians
2024 ARKIV
Gunnar Fløystad,
Cordian Riener,
Satoshi Murai,
Kohji Yanagawa
:
MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties
Mathematisches Forschungsinstitut Oberwolfach 2022 ARKIV
Hugues Verdure,
Philippe Moustrou,
Cordian Riener,
Helen Naumann,
Thorsten Theobald
:
Symmetries in AM/GM-based optimization
2021 ARKIV
Cordian Riener,
Ragni Piene
:
Ragni Piene
2020 ARKIV
Cordian Riener,
Saugata Basu,
Marie Françoise Roy
:
Foreword to the Special Issue dedicated to the Arctic Applied Algebra conference 2019 in Tromsø
Cordian Riener
:
Symmetries in algorithmic questions in real algebraic geometry
2020 ARKIV
Cordian Riener
:
Efficiently computing Betti numbers of symmetric semi algebraic sets
2020 ARKIV
Cordian Riener
:
Stand på forskningstorg (Matematiske spill og gåter) under Utforsk UiT, Forskningsdagene 2019
2019 ARKIV
Cordian Riener
:
Algorithms to compute topological invariants of symmetric semi algebraic sets
2019 ARKIV
Cordian Riener
:
Geometry of quadrature rules
2019 ARKIV
Cordian Riener
:
Vandermonde varieties, mirror spaces, and the cohomology of symmetric semi-algebraic sets
2019 ARKIV
Cordian Riener
:
Computing the homology of symmetric semi-algebraic sets
2018 ARKIV
Cordian Riener
:
Efficiently computing the Betti numbers of symmetric semi-algebraic sets
2018 ARKIV
Cordian Riener
:
Semidefinite optimization and arithmetic progressions
2018 ARKIV
Cordian Riener,
Mohab Safey el Din
:
Real Root Finding for Equivariant Semi-algebraic Systems
The 50 latest publications is shown on this page. See all publications in NVA here →
Research interests
- Positivity and sums of squares
- Symmetric semi-algebraic geometry
- Polynomial and semidefinite optimization
- Symbolic computation and computational complexity
Teaching
I teach at all levels, from first-year courses to special curricula for master's and PhD students.
Regular courses
- Real Algebraic Geometry
- Algebraic Geometry
- Algebra 1 and Algebra 2
- Calculus 3
- Linear Algebra (MAT-1004 / MAT-1020)
- Numerical Methods
Special curricula (master/PhD)
- Mathematical Optimization: Convexity, Duality, and Convexification
- Geometric Combinatorics
- Symmetry in Computation
- Invariant Theory and Representation Theory
- Semidefinite Programming and Polynomial Optimization
Online micro-courses
- MIK-1018 What Is Mathematics?
- MIK-1019 Making Optimal Decisions
Course pages and teaching material: cordian.de/teaching
Member of research group / centre
CV
Education
- 2000–2006: Mathematical economics (Wirtschaftsmathematik), Universität Ulm
- 2003–2007: Philosophy, Universität Ulm
- 2004–2005: Master 2 in pure mathematics, Université de Bordeaux 1
- 2007–2011: Dr. phil. nat. in mathematics, Goethe-Universität Frankfurt
- 2009–2014: Magister Artium in philosophy, Goethe-Universität Frankfurt
- 2018: Habilitation in mathematics, Universität Konstanz
Positions
- Since 2019: Professor of mathematics, UiT The Arctic University of Norway
- 2018–2019: Associate Professor, UiT The Arctic University of Norway
- 2016–2018: Acting Professor (W2), Universität Konstanz
- 2012–2016: Aalto Science Institute Fellow, Aalto University, Helsinki
- 2011–2012: Associate Fellow, Zukunftskolleg, Universität Konstanz
- 2007–2011: Research Assistant, Goethe-Universität Frankfurt
Service
- 2026–: Editor-in-Chief, Journal of Symbolic Computation
- 2025–: Scientific coordinator, national PhD school Mathesis
- 2024–: Co-director, Lie–Størmer Centre (UiT/UiB)
- 2023–: Chair, Norwegian Mathematics Council
- 2022–: Board of the Abel Prize
- 2022–2023: SIAM Activity Group on Algebraic Geometry (officer)
- 2021–: Pro-Dean for PhD education, Faculty of Science and Technology, UiT
- 2019–2020: Faculty Board, Faculty of Science and Technology, UiT
Supervision
PhD students
- Current: Gaël Druez, Henri Breloer, Örs Rekák, Luca Wellmeier
- 2024: Robin Schabert
- 2024: Arne Lien
- 2022: Sebastian Debus
- 2018: Jan Rolfes
Postdocs
- Philippe Moustrou, Thi Xuan Vu, Tobias Boege, Ettore Teixeira Turatti, Rodolfo Ríos-Zertuche
Master's students
- 2023: Elias Sandal, Alessandro Schena
- 2022: Ingar Wesenberg Eskeland
- 2021: Pedro González
- 2020: Arne Lien
Conferences and summer schools
I have co-organized a number of conferences, workshops and summer schools, including ISSAC 2023 and Baltic Way 2022 in Tromsø, and I chair the organizing committee of Polynomials in Tromsø (PIT 2027). Full list: cordian.de/events.