Biography
I am a professor of mathematics at UiT The Arctic University of Norway. I am currently also acting as Pro Dean for PhD education at the Faculty of Science and Technology. Currently, I have the pleasure to serve as leader of the Norwegian Mathematical Council as well as member of the board of the Abel prize.
My research interests include real algebraic geometry, optimization, computational complexity, and computer algebra. I am leading the Algebra group and I am also one of directors of the Lie-Størmer Center for Fundamental Structures in Computational and Pure Mathematics.
Download my resumé.
Interests
- Computational Complexity
- Real algebraic Geometry
- Symmetries in Computations
Education
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Habilitation in Mathematics, 2018
University of Konstanz
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Magister Artium (Philosophy), 2013
Goethe University Frankfurt
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PhD in Mathematics, 2011
Goethe University Frankfurt
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Dipl. Math. oec., 2006
Ulm University
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Master Mathematics, 2005
Université de Bordeaux
Experience
Professor
UiT The Arctic University of Norway
Vertretungsprofessur
University of Konstanz
Aalto Science Fellow
Aalto University
Postdoctoral fellow
University of Konstanz
Research Assistant
Goethe University
Projects
.js-id-poema
Featured Publications
Publications
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(2024).
On nonnegative invariant quartics in type A.
arXiv preprint arXiv:2402.03722.
(2024).
Connectivity in Symmetric Semi-Algebraic Sets.
International Symposium on Symbolic and Algebraic Computation 2024.
(2023).
The wonderful geometry of the Vandermonde map.
arXiv preprint arXiv:2303.09512.
(2023).
A semidefinite programming hierarchy for covering problems in discrete geometry.
arXiv preprint arXiv:2312.11267.
(2023).
Attitudes towards mathematics, achievement, and drop-out intentions among STEM and Non-STEM students in Norway.
International Journal of Educational Research Open.
(2023).
Faster real root decision algorithm for symmetric polynomials.
International Symposium on Symbolic and Algebraic Computation 2023.
(2023).
Polynomial Optimisation, Moments, and Applications.
Springer Optimization and Its Applications.
(2023).
Reflection groups and cones of sums of squares.
Journal of Symbolic Computation.
(2023).
Symmetric SAGE and SONC forms, exactness and quantitative gaps.
Journal of Symbolic Computation.
(2023).
Symmetries in polynomial optimization.
Polynomial Optimisation, Moments, and Applications.
(2023).
The poset of Specht ideals for hyperoctahedral groups.
Algebraic Combinatorics.
(2022).
Equivariant algebraic and semi-algebraic geometry of infinite affine space.
Journal of Algebra.
(2022).
Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions.
arXiv:2203.08727.
(2022).
Orbit Spaces of Weyl Groups Acting on Compact Tori - A Unified and Explicit Polynomial Description.
SIAM Journal on Applied Algebra and Geometry.
(2022).
# P-hardness of matrix immanants on restricted matrices..
2022 Spring Central Sectional Meeting.
(2022).
MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties.
Oberwolfach Reports.
(2021).
Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets.
Foundations of Computational Mathematics.
(2021).
Polynomial opzimization problems invariant by finite reflection groups.
2021 Joint Mathematics Meetings (JMM).
(2021).
Return of the plane evolute.
Annales de l’Institut Fourier.
(2021).
Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations.
Journal of Symbolic Computation.
(2021).
# P-hardness proofs of matrix immanants evaluated on restricted matrices.
arXiv preprint arXiv:2103.04934.
(2021).
Symmetry reduction in AM/GM-based optimization.
SIAM J. Optimization.
(2021).
Symmetric nonnegative forms and sums of squares.
Discrete & Computational Geometry.
(2020).
Generalized eigenvalue methods for Gaussian quadrature rules.
Annales Henri Lebesgue.
(2020).
On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities.
International Mathematics Research Notices.
(2020).
Reflection groups and cones of sums of squares.
arXiv preprint arXiv:2011.09997.
(2018).
On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms.
Selecta Mathematica.
(2018).
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).
Real root finding for equivariant semi-algebraic systems.
International Symposium on Symbolic and Algebraic Computation.
(2018).
Reflection groups, reflection arrangements, and invariant real varieties.
Proceedings of the AMS.
(2017).
Bounding the equivariant Betti numbers of symmetric semi-algebraic sets.
Advances in Mathematics.
(2017).
Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets.
Ordered Algebraic Structures and Related Topics, Contemporary Mathematics.
(2017).
On irreducible components of real exponential hypersurfaces.
Arnold Mathematical Journal.
(2016).
Bounds on the individual Betti numbers of complex varieties, stability and algorithms.
arXiv preprint arXiv:1606.04069.
(2016).
Deciding positivity of multisymmetric polynomials.
Journal of Symbolic Computation.
(2016).
Symmetric semi-algebraic sets and non-negativity of symmetric polynomials.
Journal of Pure and Applied Algebra.
(2013).
Exploiting symmetries in SDP-relaxations for polynomial optimization.
Mathematics of Operations Research.
(2012).
A note on extrema of linear combinations of elementary symmetric functions.
Linear and Multilinear Algebra.
(2012).
On the degree and half-degree principle for symmetric polynomials.
Journal of Pure and Applied Algebra.
(2008).
Positive Polynome und semidefinite Optimierung.
Jahresbericht der DMV.
(2006).
On extreme forms in dimension 8.
Journal de théorie des nombres de Bordeaux.
Contact
- cordian.riener@uit.no
- +47 77 64 40 90
- Forskningsparken, Tromsø, 9037
- Forskningsparken 1 4th floor B425
- DM Me
- Skype Me
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