Louis Hainaut: Postdoc day, Seminar 2: Configuration spaces on a wedge of spheres

Abstract: In joint work with Nir Gadish we study the rational cohomology with compact support of configuration spaces on a (finite) wedge of spheres. We prove that there exist universal coefficients with which these cohomology groups can be expressed as a polynomial functor of the reduced cohomology of the space. We further use this description to determine some parts of these cohomology groups and we also prove applications in other fields, such as Hochschild–Pirashvili homology, representation theory of \(\operatorname{Out}(F_g)\) or cohomology of the moduli space \(M_{2,n}\).