Title: Rational homology of configuration spaces via factorization homology
Speaker: Ben Knudsen, Northwestern
Abstract: The study of configuration spaces is particularly tractable over a field of characteristic zero, and there has been great success over the years in producing complexes simple enough for explicit computations, formulas for Betti numbers, and descriptive results. I will discuss recent work identifying the rational homology of the configuration spaces of an arbitrary manifold with the homology of a Lie algebra constructed from its cohomology. The aforementioned results follow immediately from this identification, albeit with hypotheses removed; in particular, one obtains a new, elementary proof of homological stability for configuration spaces.
