My research focusses on substructures of finite geometires, more particular about blocking sets, partial spreads and covers of finite classical polar spaces. Within the scope of that research also other topics as blocking sets of projective planes and projective spaces, en some generalizations like the so-called minihypers and partial spreads and covers of some generalized quadrangles.

Typical problems are to find characterizations and classifications of these substructures, e.g. what is the smallest blocking set of a particular polar space? We also want to investigate typical porperties: how many points does such a blocking set contain? What is the geometrical structure? Sometimes we use computeralgebra packages to find directives for the theoretical research, or to prove the existence or the non-existence of certain examples.


Blocking sets and partial spreads in finite classical polar spaces.


All publications

Selected Talks

  1. The smallest minimal blocking sets of Q(6,q), q even. slides. Combinatorics 2002, (2--8 june 2002, Maratea, Italy)
  2. The smallest sets of points meeting all generators of H(2n,q2), n ≥ 2. slides. EIDMA Symposium 2003 (13-14 november 2003, Eindhoven, The Netherlands).).
  3. Minimal blocking sets of size q2+2 of Q(4,q), q an odd prime, do not exist. slides. Incidence Geometry (23 -- 29 may 2004, La Roche, Belgium).
  4. The Hermitian variety H(5,4) has no ovoids. slides. Algebraic Combinatorics and Applications (ALCOMA05) (3--10 april 2005, Thurnau, Germany).
  5. Classification results on weighted minihypers. slides. Fourth International Workshop on Optimal Codes and related topics (17--23 june 2005, Pamporovo, Bulgaria).
  6. Large maximal partial spreads of the Hermitian variety H(5,q2). Combinatorics 2006, (june 25 --july 1st 2006, Ischia, Italy)
  7. Algebraic techniques in finite geometry: a case study. slides. Algebra seminar at UCD, Dublin, Ireland, januari 29th, 2007
  8. Lower and upper bounds of maximal partial ovoids of orthogonal polar spaces. slides. Geometric and algebraic combinatorics 2008 (17--22 august 2008, Oisterwijk, The Netherlands)
  9. Maximal partial ovoids of the generalized quadrangle Q(4,q). slides. 22nd British Combinatorial Conference (5--10 july 2009; St. Andrews, UK)
  10. On maximal partials spreads of the hermitian variety H(3,q2). slides. Algebraic Combinatorics and Applications (ALCOMA10) (11--18 april 2010, Thurnau, Germany).
  11. Point sets in AG(n,q) (not) determining certain directions. (invited talk) slides. Baer Colloquium June 2010, Ghent, Belgium, 12th june 2010.
  12. On the structure of the directions not determined by large affine point sets. slides. Finite geometries 2011 (19--25 june, Irsee, Germany)
  13. Old and new results on the MDS-conjecture. slides Incidence Geometry and Buildings, 6--10 February 2012, Ghent, Belgium
  14. Direction problems in affine spaces, related problems, and applications. slides. Academy Contact Forum Galois geometries and applications, Brussels, 5 October 2012.
  15. On Cameron-Liebler line classes with large parameter. CanaDAM 2013 (Canadian conference on Discrete and Algorithmic Mathematics. (10--16 June 2013, St. John's, NL, Canada)
  16. Segre's lemma of tangents and linear MDS codes (invited talk). slides. Journées estivales de la méthode polynomiale. (24--27 June, Lille, France)
  17. FinInG: a share package for GAP. slides. Finite geometries: Fourth Irsee Conference (14 -- 20 September 2014, Irsee, Duitsland)
  18. Tight sets in finite geometry (invited talk). slides. ALCOMA15 (15 -- 20 March 2015, Banz, Duitsland)

All talks

Upcomining Talks

  1. On the (linear) MDS conjecture (invited talk). slides. Wandering colloquium ``Getaltheorie in het vlakke land -- Arithméthique en plat pays'' (October 19, 2015, Gent, Belgium)

Supervision of PhD-theses

Mirka Cimrakova: Search algorithms for substructures in generalized quadrangles (May 19th, 2006)
Anja Hallez: Linear codes and blocking structures from finite projective and polar spaces (April 26th, 2010)
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Research Group Incidence Geometry Homepage van Jan De Beule