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FIORINI Samuel

Person in charge of the Unit : Oui

Integrating incidence geometries in the kernel of the symbolic language Magma

In collaboration with Professor John Cannon from the University of Sydney, we develop a set of procedures within the kernel of the language Magma. The aim is to extend Magma into a tool for the study of incidence geometries and of (group, geometry) pairs.

Study and classification of the residually primitive incidence geometries of the Suzuki groups

The known classiciations of the maximal subgroups of the almost simple groups of Suzuki type and their geometric interpretation in terms of Tits-Suzuki ovoids allows to start a classification of their intersections and of the related incidence geometries

To each family of relations on a finite set, one associates a polytope which is the convex hull of all the characteristic vectors of those relations. The geometry of the resulting convex polytopes is investigated, with the particular aim of producing facets. The proeminent cases are those of linear orders, weak orders, partial orders; the associated polytopes also appear in combinatorial optimization.