Université Libre de Bruxelles, Département de Mathématique

Service de Géometrie

• C. Huybrechts:
  Reduction of diagram geometries over Coxeter diagrams extended by linear spaces (joint with A. Pasini and F. Buekenhout). Constructions of diagram geometries.

• C. Cerf:
  Knot theory. Impossible figures.

• S. Lehman:
  Characterizations of point-line spaces of buildings and diagram geometries. Point-line characterization of buildings of type . Enumeration of inductively minimal geometries of given rank.

• F. Buekenhout:
  Alexandrov Geometry (joint with Ph. Masson). The flag-transitive geometries of small simple groups and primitive groups (joint with M. Dehon, Ph. Cara, D. Leemans). Study of an Ivanov-Shpectorov geometry for the O'Nan sporadic group. The small symmetric graphs and their enantiomeric labellings (joint with J. Brocas, M. Dehon). Diagram geometries with linear spaces as rank two residues (joint with C. Huybrechts).

• D. Leemans:
  Study of the residually weakly primitive flag-transitive geometries of the first Janko group , the Mathieu group and the Suzuki groups. Study of an Ivanov-Shpectorov geometry for the O'Nan sporadic group.

• Ph. Cara:
  Study of residually weakly primitive flag-transitive geometries of the alternating and symmetric groups. Study of inductively minimal geometries.

• M. Dehon:
  Study of the residually weakly primitive flag-transitive geometries of the Mathieu groups , and . The small symmetric graphs and their enantiomeric labellings (joint with J. Brocas, M. Dehon).

Computer Algebra
Research activities on computer algebra about the solutions of nonlinear systems of differentials equations. The activities are centered around a European working group: CATHODE (computer algebra tools for handling ordinary differential equations). We try to construct algoritms for solving systems of D.E. appearing in various domains in physics.