Applied and Computational Algebra

My research concerns both theoretical and computational questions in several topics, ranging from number theory to polynomial optimization, going through discrete geometry, coding theory and real algebraic geometry. I am particularly excited by questions involving lattices and sphere packings.

For more information, see here.

Contact:

E-mail: pmo025@post.uit.no

Work phone: +4777644078

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Hans Munthe-KaasProfessor

Hans Munthe-Kaas – Professor

Research interests:

Computational mathematics: geometric integration, Lie theory, applied group theory, approximation theory, harmonic analysis and signal processing

Differential geometry and algebra: algebras of connections on manifolds, combinatorics of formal flows of differential equations and structure preserving discretisations

Contact:

Position: Professor

E-mail: hans.z.munthe-kaas@uit.no

Private phone: 45238987

Link to employee page (Hans Munthe-Kaas)

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Ettore Teixeira TurattiPostdoctoral Fellow

Ettore Teixeira Turatti – Postdoctoral Fellow

Contact:

Position: Postdoctoral Fellow

E-mail: ettore.t.turatti@uit.no

Link to employee page (Ettore Teixeira Turatti)

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Örs RebákDoctoral Research Fellow

Örs Rebák – Doctoral Research Fellow

Contact:

Position: Doctoral Research Fellow

E-mail: ors.rebak@uit.no

Link to employee page (Örs Rebák)

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Fatemeh Mohammadi

Contact:

E-mail: fatemeh.mohammadi@uit.no

Link to employee page (Fatemeh Mohammadi)

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Xuan Thi VuPostdoctoral Fellow

Xuan Thi Vu – Postdoctoral Fellow

Contact:

Position: Postdoctoral Fellow

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Cordian RienerProfessor (Group leader)

Cordian Riener – Professor

Research interests:

Real Algebraic Geometry, Optimization, Computational Algebra, Computational Complexity Theory

Contact:

Position: Professor

E-mail: cordian.riener@uit.no

Work phone: +4777644090

Link to employee page (Cordian Riener)

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Elias Sandal

Contact:

E-mail: elias.sandal@uit.no

Link to employee page (Elias Sandal)

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Andréa BaldiResearch Assistant

Andréa Baldi – Research Assistant

Contact:

Position: Research Assistant

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Publications

Here are recent preprints and publications by our members.

Publications

Toric degenerations of flag varieties from matching field tableaux, O. Clarke, F. Mohammadi, Journal of Pure and Applied Algebra, Volume 225, Issue 8, August 2021, 106624

Standard monomial theory and toric degenerations of Schubert varieties from matching field tableaux, O. Clarke, F. Mohammadi, Journal of Symbolic Computation, Volume 104, May–June 2021, Pages 683-723

Coloring the Voronoi tessellation of lattices, M. Dutour Sikirić, D. Madore, P. Moustrou, F. Vallentin, to appear in Journal of the London Mathematical Society, 2021

Conditional probabilities via line arrangements and point configurations, O. Clarke, F. Mohammadi, H. Motwani, to appear in Linear and Multilinear Algebra, 2021

Exact semidefinite programming bounds for packing problems, M. Dostert, D. de Laat, P. Moustrou, to appear in SIAM Journal on Optimization, 2021

Combinatorial Mutations and Block Diagonal Polytopes, O. Clarke, A. Higashitani, F. Mohammadi, Collectanea Mathematica, 2021

Higher weight spectra of codes from Veronese threefolds, T. Johnsen, H. Verdure, Journal of Pure and Applied Algebra, 225, 2021

Symmetric ideals, Specht polynomials and solutions to symmetric systems of equations, P. Moustrou, C. Riener, H. Verdure, Journal of Symbolic Computation 107, 106 - 121, 2021

On the isotypic decomposition of cohomology modules of symmetric semi-algebraic sets: polynomial bounds on multiplicities, S. Basu, C. Riener. International Mathematics Research Notices 2020 (7), 2054–2113, 2020

Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux, O. Clarke, F. Mohammadi, Journal of Algebra, Volume 559, 1 October 2020, Pages 646-678

Greedy weights for matroids, T. Johnsen, H. Verdure, Design, Codes and Cryptography 89 pp 387-405, 2020

Conditional independence ideals with hidden variables, O. Clarke, F. Mohammadi, J. Rauh, Advances in Applied Mathematics, Volume 117, June 2020, 102029

A polymatroid approach to generalized weights of rank metric codes, S. Ghorpade, T. Johnsen, Design, Codes and Cryptography 88 pp 2531-2546, 2020

Generalized eigenvalue methods for Gaussian quadrature rules, G. Blekherman, M. Kummer, C. Riener, M. Schweighofer, C. Vinzant, Annales Henri Lebesgue 3, 1327–1341, 2020

Higher weight spectra of Veronese codes, T. Johnsen, H. Verdure, IEEE, transactions on Information Theory 66 (6) pp 3538 - 3546, 2020

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Preprints

# P-hardness proofs of matrix immanants evaluated on restricted matrices, I. Miklos, C. Riener, 2021

Symmetry reduction in AM/GM-based optimization, P. Moustrou, H. Naumann, C. Riener, T. Theobald, H. Verdure, 2021

Reflection groups and cones of sums of squares, S. Debus, C. Riener, 2020

Triangulations and Canonical Forms of Amplituhedra: a fiber-based approach beyond polytopes, F. Mohammadi, L. Monin, M. Parisi, 2020

Standard monomial theory and toric degenerations of Richardson varieties inside Grassmannians and flag varieties, N. Chary Bonala, O. Clarke, F. Mohammadi

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Seminar

Our seminar takes place every second week, on Friday, 2-3 p.m., in a hybrid form. If you wish to attend and/or give a talk, please contact Philippe Moustrou and/or Cordian Riener.

Next talk: June, 18th - Prasant Singh

June, 18th: Prasant Singh, UiT the Arctic University of Norway

Title: Symmetric determinental codes

Abstract:

The talk is a continuation of Prof Trygve's talk in the Bergen seminar this April,

and of what he (at least) mentioned in the Algebra seminar last week, although the talk will be self-contained.

In this talk, we recall the definition of determinantal varieties in the space of symmetric matrices.

Restricting the definition to finite fields, we can consider the algebraic-geometric (AG) codes arising from these varieties.

We study some interesting properties of these codes and show that these codes have only a few distinct possible weights.

In the end, we discuss the minimum distance of these codes in the even rank case, i.e., in the case when the varieties

are the zero sets of minors of odd order of a generic symmetric matrix.

The talk is based on joint work with Prof. P. Beelen (DTU) and Prof. T. Johnsen.

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Upcoming talks

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Past talks

15/06/21 - Andréa Baldi, UiT the Arctic University of Norway: From classic to post-quantum cryptography

28/05/21 - Trygve Johnsen, UiT the Arctic University of Norway: Codes and symmetries

30/04/21 - Thi Xuan Vu, UiT the Arctic University of Norway: Computing critical points for invariant algebraic systems

16/04/21 - Rakhi Pratihar, UiT the Arctic University of Norway: An overview of the notion of shellability and its applications

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