Excellence Initiative - Research University HR Excellence in Research
ul. Chopina 12/18, 87-100 Toruń
tel.: +48 56 611 3410
e-mail: wmii@mat.umk.pl
zdjęcie nagłówkowe

About the unit

Research topics

Computational mathematics, scientific computations and constructive and algorithmic problem solving in various branches of mathematics and its applications. Combinatorial problems (including graph theoretic problems) and symbolic computations. Problems of computability, computational complexity and efficient computer implementations.

Recently, research has been conducted mainly in the following two areas:

  1. Development of combinatorial and algorithmic methods concerning integer matrices, quadratic and bilinear forms, Diophantine equations and related graph structures. In particular, the study of discrete structures and combinatorial problems derived from the representation theory of associative algebras over a field and the theory of Lie algebras.

  2. Study of algebraic and geometric properties of invariant subspaces of nilpotent linear operators using combinatorial tools (e.g. Littlewood-Richardson tableaux, standard Young tableaux, arc diagrams). Study of analogous problems, including Birkhoff-type problems, for abelian groups and modules over discrete valuation rings.

    

    

    3. 



Papers related to research issues


The research results of the department’s employees are published in international mathematical and computer science journals, including those indexed in the DBLP database, as well as in computer science conference publications.


The most important recent papers


    

  1. Mróz A., Zając K., Weak Dynkin type and the universality of non-negative Coxeter-regular integral quadratic forms, Documenta Mathematica 30 (2025), 245–274,  DOI: 10.4171/DM/994
    2. 

  2. Kaniecki M., Mikulski Ł.: On categorical approach to reaction systems, Natural Computing, vol. 23, 2024, s. 295–307, DOI: 10.1007/s11047-024-09978-1
    3. 

  3. Gąsiorek M.: Congruence of rational matrices defined by an integer matrix, Applied Mathematics and Computation, vol. 440, 2023, s. 1-15, DOI:10.1016/j.amc.2022.127639
    4. 

  4. Simson D.: Weyl orbits of matrix morsifications and a Coxeter spectral classification of positive signed graphs and quasi-Cartan matrices of Dynkin type An, Advances in Mathematics 404, 2022, 108389.
    5. 

  5. Kosakowska J., Schmidmeier M.: The socle tableau as a dual version of the Littlewood–Richardson tableau, Journal of the London Mathematical Society-Second Series, vol. 106, nr 2, 2022, s. 1357-1379, DOI:10.1112/jlms.12601
    6. 

  6. Simson D., Zając K.: Applications of mesh algorithms and self-dual mesh geometries of root Coxeter orbits to a Horn-Sergeichuk type problem, Linear Algebra and Its Applications, vol. 632, 2022, s. 79-152, DOI:10.1016/j.laa.2021.09.005
    7. 

  7. Mróz A., Zając K.: Weyl roots and equivalences of integral quadratic forms, Linear Algebra and Its Applications, vol. 650, 2022, s. 210-235, DOI:10.1016/j.laa.2022.06.007
    8. 

  8. Makuracki B., Mróz A.: Quadratic algorithm to compute the Dynkin type of a positive definite quasi-Cartan matrix, Mathematics of Computation, vol. 90, nr 327, 2021, s. 389-412, DOI:10.1090/mcom/3559
    9. 

  9. Simson D.: A Coxeter spectral classification of positive edge-bipartite graphs. 2: Dynkin type Dn;, Linear Algebra and Its Applications, vol. 612, 2021, s. 223-272, DOI:10.1016/j.laa.2020.11.001
    10. 

  10. Celikbas E., Laxmi J., Kraśkiewicz W., Weyman J.: The family of perfect ideals of codimension 3, of type 2 with 5 generators, Proceedings of the American Mathematical Society, vol. 148, nr 7, 2020, s. 2745-2755, DOI:10.1090/proc/14646
    11. 

  11. Kaniecki M., Kosakowska J.: Applications of Littlewood-Richardson tableaux to computing generic extension of semisimple invariant subspaces of nilpotent linear operators, Linear Algebra and Its Applications, vol. 588, 2020, s. 134-159, DOI:10.1016/j.laa.2019.11.019
    12. 

  12. Kosakowska J., Schmidmeier M., Thomas H.: Two partial orders for standard Young tableaux. Electronic Journal of Combinatorics, vol. 26, 2019, 1–18.
    13. 

  13. Kosakowska J., Schmidmeier M.: The boundary of the irreducible components for invariant subspace varieties, Mathematische Zeitschrift, vol. 290, nr 3-4, 2018, s. 953-972, DOI:10.1007/s00209-018-2047-8
    14. 

  14. Kosakowska J., Schmidmeier M.: Operations on arc diagrams and degenerations for invariant subspaces of linear operators, Transactions of the American Mathematical Society, vol. 367, nr 8, 2015, s. 5475-5505, DOI:10.1090/S0002-9947-2014-06206-5
    15. 

  15. Bocian R., Felisiak M., Simson D.: Numeric and mesh algorithms for the Coxeter spectral study of positive edge-bipartite graphs and their isotropy groups, Journal of Computational and Applied Mathematics, vol. 259, 2014, s. 815-827, DOI:10.1016/j.cam.2013.07.013
    16. 



A full list of over 270 publications by the department’s staff is available at Research Portal.