Jeudi 31 Mars
Heure: 
10:15  12:00 
Lieu: 
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 
Résumé: 
Topologie algébrique  The psubgroup posets and Quillen's conjecture  
Description: 
Kevin Piterman The psubgroup complexes have been largely studied in connection with group cohomology, finite group theory (including the Classification), representation theory, homotopy theory, etc.&nbsp;In this talk, we will mainly focus on&nbsp;understanding the homotopy type of the poset Ap(G) of nontrivial elementary abelian psubgroups of a finite group G for a given prime p. This poset was introduced by D. Quillen, who established many connections between intrinsic algebraic properties of G and homotopical properties of Ap(G). In this context, Quillen proved that if Ap(G) has a fixed point by the action of G (that is, a nontrivial normal psubgroup) then it is contractible. He conjectured the converse given rise to the wellknown Quillen's conjecture. Although there have been important advances on the conjecture, it is still open. For example, one of the major advances was achieved by AschbacherSmith: they established the conjecture for p&gt;5, under certain restrictions on the finite unitary groups. During the talk, I will present some new developments and results on the conjecture, obtained in collaboration with Stephen D. Smith. In particular, we will see that AschbacherSmith's theorem can be extended to every odd prime p, and also to p=2 (modulo further restrictions on some simple groups). These results rely on making suitable homotopical replacements of Ap(G) by some nonstandard psubgroup&nbsp;posets, which lead to new ways of understanding the homotopy type of these objects. 

