Personnel composition:
Jiří Klaška, Miroslav Kureš (leader), Jiří Tomáš, as well as doctoral and master's students

Annotation:
Various questions related to the properties of polynomial algebras, including the study of F-rational points, irrationalities, factorization of algebras, homomorphisms of factor (Weil) algebras, etc., with the aim of applying algebraic methods mainly in differential geometry, but also in some problems of algebraic and Diophantine geometry. Use in a range of disciplines from mechanics to cryptography.

Selected recent publications:
Maya, B., Kureš, M., Some tridiagonal matrices and determinants of Schur-Cohn criterion for trinomials, Scientif. Bull. P. U. B. Ser. A, accepted for publication
Navrátil, D., Matrix representation of third order jet groups, Annales U.M.C.S., accepted for publication
Kureš, M., On coordinate expressions of jet groups and their representations, Geom.   Integr. Quant. 2021
Kureš, M., Skula, L., Reduction of matrices over orders of imaginary quadratic field. Tench. Alg. Appl. 2011
Klaška, J., Quartic polynomials with a given discriminant. Math. Word. 2022
Klaška, J. Skula, L., Law of inertia for the factorization of cubic polynomials – the real case. Util. Math. 2017
Tomáš, J., The general rigidity result for bundles of A-covelocities and A-jets, Czech. Math. J. 2017
Tomáš, J., Bundles of (p,A)-covelocities and (p.A)-jets, Miskolc Math. N. 2013

Assigned doctoral topics:
Algebras of dual numbers and their generalization, use in screw calculus, PhD student Baraah Maya, supervisor Miroslav Kureš
Algebraic-geometric methods in continuum mechanics and materials with microstructure, doctoral student Dušan Navrátil, supervisor Miroslav Kureš
Homogeneous spaces and foliation from the point of view of the theory of jet spaces and Weil functors and their physical applications, PhD student Filip Petrák, supervisor Jiří Tomáš

Examples of defended diploma and bachelor theses:
Algebraic methods for solving cubic equations, bachelor thesis, author Vladimíra Sladká, supervisor Jiří Klaška
Two types of septic trinomials and their use in hyperelliptic cryptography, author Adéla Felcmanová, supervisor Miroslav Kureš
Lie groups from the point of view of kinematics and applications in robotics, diploma thesis, author Jan Kalenský, supervisor Jiří Tomáš

Cooperation:
École spéciale militaire de Saint-Cyr, France