# Jan DE BEULE

## Biography

Jan De Beule obtained a PhD in Mathematics from Ghent University (Belgium) in 2004. In the period 2004 — 2015 he was affiliated with Ghent University, supported in 2009 — 2015 by a junior and senior postdoctoral fellowship of the Research Foundation Flanders (Belgium)(FWO). He worked together during long research stays with researchers in Germany, Hungary, Spain, Australia and New Zealand. He joined the Department of Mathematics and Data Science of the VUB in October 2015 as researcher, with teaching duties in both the faculties of Sciences and Bio-Engineering Sciences and Engineering Sciences. Since March 1st he is full-time assistant professor in the department of Mathematics and Data Science of the faculty of Sciences and Bio-Engineering Sciences. His field of research is discrete mathematics, with applications in data science, and a particular focus on finite geometry, graph theory, coding theory and computer algebra.

## Location

PLEINLAAN 2

1050 BRUSSEL

Belgium

## RESEARCH

The foundations of finite geometry are amongst others, the work of the Italian mathematician Beniamino Serge (1903 — 1977) and the Belgian mathematician Jacques Tits (1930 — 2021). Segre studied arcs and caps in finite projective spaces from the viewpoint of classical algebraic geometry. He formulated an important conjecture on so-called Maximum Distance Separable Codes, a family of codes later used in many applications.

Jacques Tits developed a geometrical interpretation of finite simple groups. Remarkably, the objects of interest in the work of Segre, ovals and ovoids, play also in the work of Tits a major role. Both lines of research together focus on a combinatorial and algebraic study of classical geometrical objects over finite fields, and this initiated a field of research now known as finite geometry.

Structures in finite geometry, such as finite projective spaces and finite polar spaces yield highly symmetric and regular graphs. So it is not surprising that finite geometry and graph theory are by now intertwined. Strongly regular graphs, distance regular graphs, association schemes, and finally coherent configurations then yield commutative and non-commutative matrix algebras. It turns out that their representations play an important role in to study the corresponding geometric structures.

Applications of finite geometry are found in coding theory and cryptography. Particular structures in finite geometries give rise to new classes of codes, and particular classes of linear codes derived from geometric structures, are important in post-quantum cryptography. Finally, the role of computational mathematics has been increasing in this research. There are by now advanced possibilities to study an explore geometric structures interactively, and there is a plethora of possibilities to exhaustively explore a search space to find an answer on characterization and classification questions. The development of tailor made software is part of the research.

## TEACHING

- Analysis Part I, Analysis Part II, Analysis Part III, Linear Algebra Part I, Linear Algebra Part II: bridging courses for students Master Biomedical Engineering

- Mathematics for Data Science: compulsory course for first year students in the bachelor curriculum Mathematics and Data Science

- Mathematics: calculus and linear algebra: partim linear algebra: compulsory course in mathematics for all first year students in sciences

- Computeralgebra: foundations and applications: elective course in the master curriculum mathematics.