About Me

Education & employment

Research

Research interests

• Twisted conjugacy and related topics (e.g. Reidemeister-Nielsen fixed point theory)
• Nilpotent-by-finite and polycyclic-by-finite groups
• Zeta functions of groups
• Computational group theory, in particular through the use of GAP

Articles

• Twisted conjugacy and separability. Preprint (2024).

    A group G is twisted conjugacy separable if for every automorphism φ, distinct φ-twisted conjugacy classes can be separated in a finite quotient. Likewise, G is completely twisted conjugacy separable if for any group H and any two homomorphisms φ,ψ from H to G, distinct (φ,ψ)-twisted conjugacy classes can be separated in a finite quotient. We study how these properties behave with respect to taking subgroups, quotients and finite extensions, and compare them to other notions of separability in groups. Finally, we show that for polycyclic-by-nilpotent-by-finite groups, being completely twisted conjugacy separable is equivalent to all quotients being residually finite.
  arXiv:2305.01583 PDF
• Extreme Reidemeister spectra of finite groups. To appear in: Topology and its Applications (2024).

    We extend the notions of "R∞-property" and "full (extended) Reidemeister spectrum" to finite groups in a meaningful way. We provide examples of finite groups admitting these properties, if they exist, by looking at groups of small order as well as (quasi)simple groups.
  arXiv:2311.12594 PDF
• The Reidemeister Spectra of Low Dimensional Almost-Crystallographic Groups. In: Experimental Mathematics 31.2 (2022), pp. 444-455.

    We determine which non-crystallographic, almost-crystallographic groups of dimension 4 have the R∞-property. We then calculate the Reidemeister spectra of the 3-dimensional almost-crystallographic groups and the 4-dimensional almost-Bieberbach groups.
  10/grv3jv Zbl  07566893  MR4458123 arXiv:1901.05393 PDF
• Algorithms for twisted conjugacy classes of polycyclic-by-finite groups (with K. Dekimpe). In: Topology and its Applications 293 (2021), 107565.

    We construct two practical algorithms for twisted conjugacy classes of polycyclic groups. The first algorithm determines whether two elements of a group are twisted conjugate for two given endomorphisms, under the condition that their Reidemeister coincidence number is finite. The second algorithm determines representatives of the Reidemeister coincidence classes of two endomorphisms if their Reidemeister coincidence number is finite, or returns "false" if this number is infinite. We also discuss a theoretical extension of these algorithms to polycyclic-by-finite groups.
  10/grvpwc Zbl  07331374  MR4229472 arXiv:2002.08285 PDF
• Fixed points of diffeomorphisms on nilmanifolds with a free nilpotent fundamental group (with K. Dekimpe and A. R. Vargas). In: The Asian Journal of Mathematics 24.1 (2020), pp. 147-164.

    Let M be a nilmanifold with a fundamental group which is free 2-step nilpotent on at least 4 generators. We will show that for any nonnegative integer n there exists a self-diffeomorphism hn of M such that hn has exactly n fixed points and any self-map f of M which is homotopic to hn has at least n fixed points. We will also shed some light on the situation for less generators and also for higher nilpotency classes.
  10/grvpwd Zbl 1452.55001 MR4143986 arXiv:1710.09662 PDF
• The Reidemeister spectra of low dimensional crystallographic groups (with K. Dekimpe and T. Kaiser). In: Journal of Algebra 553 (2019), pp. 353-375.

    In this paper we study the number of twisted conjugacy classes (the Reidemeister number) for automorphisms of crystallographic groups. We present two main algorithms for crystallographic groups whose holonomy group has finite normaliser in GLn(ℤ). The first algorithm calculates whether a group has the R∞-property; the second calculates the Reidemeister spectrum. We apply these algorithms to crystallographic groups up to dimension 6.
  10/grv26v Zbl 1485.20129 MR3987331 arXiv:1709.07649 PDF
• Reidemeister spectra for solvmanifolds in low dimensions (with K. Dekimpe and I. Van den Bussche). In: Topological Methods in Nonlinear Analysis 53.2 (2019), pp. 575-601.

    The Reidemeister number of an endomorphism of a group is the number of twisted conjugacy classes determined by that endomorphism. The collection of all Reidemeister numbers of all automorphisms of a group G is called the Reidemeister spectrum of G. In this paper, we determine the Reidemeister spectra of all fundamental groups of solvmanifolds up to Hirsch length 4.
  10/grvprn Zbl  07130711  MR3983986 arXiv:1711.08650 PDF
• Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational (with K. Dekimpe and I. Van den Bussche). In: Communications in Algebra 46.9 (2018), pp. 4090-4103.

    We prove that the Reidemeister zeta functions of automorphisms of crystallographic groups with diagonal holonomy ℤ2 are rational. As a result, we obtain that Reidemeister zeta functions of automorphisms of almost-crystallographic groups up to dimension 3 are rational.
  10/grv3jt Zbl 1473.20055 MR3820618 arXiv:1710.02335 PDF

Software

• TwistedConjugacy, Computation with twisted conjugacy classes. GAP Package, version 2.2.0 (2024).
  GitHub 38068
• SmallClassNr, Library of finite groups with small class number. GAP Package, version 1.1.1 (2023).
  GitHub

Theses

• Reidemeister spectra for almost-crystallographic groups (supervisor: K. Dekimpe). PhD thesis. KU Leuven (2019).
  PDF
• Lagrangian submanifolds of complex space forms: parallelity conditions and curvature inequalities (supervisor: J. Van der Veken). MSc thesis. KU Leuven (2015).
  PDF

Teaching

2019 - 2020

• Geometry II

2018 - 2019

• Complex Analysis
• Final Project
• Fundamentals for Computer Science
• Geometry II
• ICT: Technical Scientific Computing

2017 - 2018

• Fundamentals for Computer Science
• Geometry II
• ICT: Technical Scientific Computing
• Mathematical Reasoning

2016 - 2017

• Geometry II
• ICT: Technical Scientific Computing
• Mathematical Reasoning
• Mathematics
• Science Communication

2015 - 2016

• Analysis and Calculus
• Geometry II
• ICT: Technical Scientific Computing
• Mathematical Methods for Biomedical Sciences
• Mathematical Reasoning
• Mathematics
• Problem Solving and Design, Part 1

Contact

• Mathematics, KU Leuven Kulak Kortrijk Campus
• Etienne Sabbelaan 53
• PO Box 7659
• 8500 Kortrijk
• Belgium