MIT Combinatorics Seminar

Incidence Geometry, Finite Group Theory And Computational Algebra

Dimitri Leemans (Université de Bruxelles and Northeastern University)

Wednesday, October 5, 2005   4:30 pm    Room 2-142


Following Jacques Tits' geometric interpretation of the exceptional complex Lie groups, Francis Buekenhout generalized in the late seventies certain aspects of this theory in order to achieve a combinatorial understanding of all finite simple groups. Since then, two main traces have been developed in diagram geometry. One is to classify geometries over a given diagram, mainly over geometries extending buildings. Another trace is to classify coset geometries for a given group under certain conditions.

We will start the talk by explaining what an incidence geometry is. Then we will give some examples of results obtained in the first and the second approach. We will explain the connection between incidence geometries and finite groups which essentially arise as automorphism groups. We will also show how computational algebra softwares like {\sc Magma} may be used to explore incidence geometries and insist on the fact that experimental work in this field has already been very fruitful and has led to several theoretical results.