Louis Hainaut: Configuration spaces on a wedge of spheres via their compactly supported cohomology

Abstract: 

For X a wedge of g circles, its compactly supported cohomology \(H_c^i(F(X, n), \mathbb{Q})\) is a representation of \(\operatorname{Out}(F_g)\). There exists a natural filtration of these groups according to which these representations factor as a representation of \(\operatorname{GL}(g)\) on each graded piece. More generally if X is any (finite) wedge of spheres there exists a similar filtration on \(H_c^i(F(X, n), \mathbb{Q})\) and the structure of each graded piece is determined by the \(\operatorname{GL}(g)\)-representations for the wedges of circles.

In this talk I will present some results obtained by Nir Gadish and me about those groups and discuss connections with other mathematical objects of interest.