Homepage van Jan De Beule



Research

Research topics

  • Research in discrete mathematics, focus on finite geometry, (applications in) coding theory and cryptography and the use of algebraic techniques.
  • Research interest in computeralgebra and computational mathematics, development of particular algorithms to investigate finite geometrical structures.

PhD thesis

Blocking sets and partial spreads in finite polar spaces

Publications

Click here for a complete list of publications

Talks

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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 (invited talk). 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 juni 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 juni, 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, Germany)
  19. Arcs in vector spaces over finite fields (invited talk). slides. Combinatorics 2016 (30 May -- 04 June 2016, Maratea, Italy)
  20. On the (weak) cylinder conjecture (invited talk). slides. Finite Geometry Workshop 2017 (28 April -- 01 May 2017, Szeged, Hungary)
  21. Finite Geometry in GAP (invited lecture). slides. GAP in Algebraic Research (18 -- 22 November 2018, Aachen, Germany)
Click here for a complete list of talks

Upcoming talks

Supervised PhD students


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