Discrete Algebra and Geometry

  • P.O. Box 513, Department of Mathematics and Computer Science

    5600 MB Eindhoven

    Netherlands

  • Groene Loper 5, MetaForum

    5612 AP Eindhoven

    Netherlands

Organization profile

Introduction / mission

Discrete mathematics is the study of objects and structures that are fundamentally discrete - made up of distinct and separated parts - as opposed to continuous.

Highlighted phrase

Developing mathematics to describe structures limited to integers

Organisational profile

This area of mathematics that has become increasingly important in recent decades, in part due to the advent of computers, and in part because of the recent ubiquity of large discrete (social, biological, ecological etc.) networks.

Discrete mathematics has many real-world applications in areas such as logistics, engineering, cryptography, computer algorithms, computer vision and relational databases. Applications vary from finding an optimal railway schedule, securing your privacy in WhatsApp, or protecting your data on a memory device against physical damage.

Describing the algebraic and geometric aspects of discrete structures in mathematics and its application areas involves objects such as finite fields, graphs, (zero sets of) polynomials, groups, algebras, and symbolic computations. The Discrete Algebra and Geometry group at TU/e develops the mathematics needed for such a description. The group plays a leading role in algebraic graph theory, combinatorics, finite and incidence geometry, group theory, discrete Lie theory and applied algebra. Team members are active in the fields of computer algebra, interactive mathematics, and applied and discrete aspects of algebraic geometry.

Recent research themes include the study of simple groups and simple Lie algebras by geometric methods, of special subsets in finite projective planes (or spaces), and of solving large systems of polynomial equations with symmetry. The group is also involved in innovation of (mathematics) education, for which it develops, experiments with and implements new forms. This includes open source software for interactive (mathematical) documents on the web, and research into the set-up of such documents and their use. The group offers this software and other open source tools for education to the larger TU/e community and beyond (e.g. 4TU.AMI institute). These activities resulted in the company Sowiso, specialized in digital testing of mathematics.

The group collaborates closely with researchers from the University of Ghent, University of Birmingham, University of Bern, Eötvös Loránd University of Budapest and 4TU.AMI (the mathematics institute of Delft University of Technology, University of Twente, Wageningen University and TU/e). Within TU/e’s mathematics department, the team is closely connected to the Coding & Cryptology group, and the Discrete Optimization group.

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    Research Output

    Cameron-Liebler sets of k-spaces in PG(n,q)

    Blokhuis, A., De Boeck, M. & D'haeseleer, J., 15 Aug 2019, In : Designs, Codes and Cryptography. 87, 8, p. 1839–1856 18 p.

    Research output: Contribution to journalArticleAcademicpeer-review

  • 1 Citation (Scopus)
    1 Downloads (Pure)

    Inherited conics in Hall planes

    Blokhuis, A., Kovács, I., Nagy, G. P. & Szőnyi, T., 1 Apr 2019, In : Discrete Mathematics. 342, 4, p. 1098-1107 10 p.

    Research output: Contribution to journalArticleAcademicpeer-review

  • 2 Downloads (Pure)

    Polynomials and tensors of bounded strength

    Bik, A., Draisma, J. & Eggermont, R. H., 1 Nov 2019, In : Communications in Contemporary Mathematics. 21, 7, 19 p., 1850062.

    Research output: Contribution to journalArticleAcademicpeer-review

  • Prizes

    NWO Vidi Award : Finite thanks to symmetry

    J. Draisma (Recipient), 2010

    Prize: NWOVidiScientific

  • Stability and structure in infinite-dimensional spaces

    R.H. Eggermont (Recipient), 2018

    Prize: NWOVeniScientific

  • Student theses

    A characterization of the special linear and unitary Lie algebra via its extremal geometry

    Author: Oostendorp, M., 31 Aug 2018

    Supervisor: Cuypers, F. (Supervisor 1)

    Student thesis: Master

    File

    A group-theoretical analysis of solvability, solutions and solution strategies of permutation puzzles

    Author: Rijpert, D. T., 15 Aug 2019

    Supervisor: Cuypers, H. (Supervisor 1)

    Student thesis: Bachelor

    File

    Continued fractions and an approximation of p-adic numbers

    Author: Verhaegh, W. A., 31 Aug 2018

    Supervisor: de Weger, B. (Supervisor 1) & Blokhuis, A. (Supervisor 1)

    Student thesis: Bachelor

    File