Ricardo Andrade: The homotopy dimension of configuration spaces of manifolds

The space of configurations of points in a manifold is, of course,  homotopy equivalent to a cell complex. Our guiding question will be:  What is the smallest dimension of such a complex? The basic theory of  configuration spaces readily produces a lower bound for that  dimension. This lower bound happens to be sharp in many examples, as  can be shown using certain homotopical decompositions of configuration  spaces. I intend to illustrate the strong geometric intuition behind  these decompositions.