Mail : marc.cabanes (at) imj-prg.fr
Bureau: Batiment Sophie Germain (8, place Aurélie Nemours), 75013 Paris , 6 ème étage, bureau 608
Telephone: (33) 1 57 27 91 46, mobile : (33) 6 30 20 22 20
My primary interest was in finite groups. A group is a fascinating object, being very constraint, almost impossible, yet some simple groups have just a finite number of elements. As anyone knows, finite groups are either solvable or contain in a distinguished way subgroups that are finite versions of Lie groups.
This is my reason for having worked mainly on finite groups of Lie type and their representations. More precisely : modular representations or modular aspects of ordinary representations of finite reductive groups. Enguehard and I tried to give an introduction to the whole subject in our book : "Representation theory of finite reductive groups", Cambridge, 2004.
Recent work by several authors has shown that most well-known conjectures on representations of finite groups can be deduced from so-called "inductive" statements on quasi-simple groups. This is due to Isaacs-Malle-Navarro (2007) for McKay's conjecture on character degrees, Navarro-Tiep (2011) for Alperin's weight conjecture, Späth (2012) for their block versions, Navarro-Späth (2013) for Brauer's height zero conjecture. In joint work with Späth, I am involved in checking the inductive statements for McKay conjecture in the not known cases of groups of Lie type for non-defining primes (the current state of this checking).
Ever tried ? Ever failed ? No matter. Try Again. Fail again. Fail better. (Samuel Beckett)