Research group algebra

Jeroen Meulewaeter

Between 2017 and 2021, I was a Ph.D. Fellow for the FWO (Science Foundation of Flanders, Belgium) under supervision of Tom De Medts with Hendrik Van Maldeghem as co-supervisor. I obtained my Ph.D. in Sciences: Mathematics in December 2021. During my PhD I was a member of the Department of Mathematics: Algebra and Geometry at Ghent University.

Research

We investigate the connection between a class of non-associative algebras known as structurable algebras and linear algebraic groups (over arbitrary fields) and related group-theoretical structures such as Moufang sets (this is a class of doubly transitive permutation groups, introduced by Jacques Tits) and buildings (also introduced by Jacques Tits) and related point-line geometries. In particular, we make use of Jordan algebras, quadratic forms, and other algebraic objects related to linear algebraic groups. We are particularly interested in exceptional buildings.

Education

  • Bachelor of Mathematics, Ghent University, 2012-2015, summa cum laude.
  • Master of Mathematics, Ghent University, 2015-2017, summa cum laude.
  • Erasmus stay at the University of Bonn, October 2015-February 2016.

Research stays

  • Eindhoven University of Technology, 5-23 November 2018, with Hans Cuypers as host.
  • Malaga University, 14-18 October and 4-8 November 2019, with Cristina Draper and Antonio Fernandez as hosts.
  • University of Zaragoza, 21-31 October 2019, with Alberto Elduque as host.

Talks

Attended conferences, workshops and summer schools

  • Buildings 2015, 28-30 September 2015, Münster.
  • Panorama of Mathematics, 21-23 October 2015, Bonn.
  • Buildings 2017, 3-5 October 2017, Münster.
  • Reinhold-Baer-Kolloquium, 20 January 2018, Braunschweig.
  • Reinhold-Baer-Kolloquium, 23 June 2018, Würzburg.
  • Simple Groups: New Perspectives and Applications, 29-31 August 2018, Bristol.
  • Groups, Geometry and Representations, 3-7 September 2018, Oxford.
  • Buildings 2018, 4-6 October 2018, Münster.
  • II International workshop on non-associative algebras, 28 April-3 May 2019, Porto.
  • Summer School on finite groups and related geometrical structures, 19-23 August 2019, Venice.
  • Workshop Groups and Geometries, 25-30 August 2019, Banff.
  • Buildings 2019, 30 September-2 October 2019, Magdeburg.
  • Mini-workshop: Rank one groups and exceptional algebraic groups, 10-16 November 2019, Oberwolfach.

Articles

  • Geometries from structurable algebras and inner ideals, Oberwolfach Reports, vol. 16, no. 4. European Mathematical Society, Berlin, pp. 3257-3260, 2019. DOI link.
  • Extremal elements in Lie algebras, buildings and structurable algebras, joint with Hans Cuypers, Journal of Algebra, vol. 580, pp. 1-42, 2021. DOI link.
  • Inner ideals and structurable algebras: Moufang sets, triangles and hexagons, joint with Tom De Medts, submitted. Preprint.
  • Convex subspaces of Lie incidence geometries, joint with Hendrik Van Maldeghem, submitted.

Teaching

I was responsible for the exercise sessions of the following courses at Ghent University:

  • Algebra II (academic years 2017-2018, 2018-2019, 2019-2020 and 2020-2021): for bachelor students in mathematics (3rd year, 2nd semester), the course notes (in Dutch) are available here.
  • Linear Algebraic Groups (academic years 2017-2018, 2018-2019 and 2019-2020): for master students in mathematics (2nd semester), the course notes are available here.

Some useful links