Moduli spaces of high-dimensional manifolds
I will explain recent and ongoing work with Soren Galatius, in which we study the cohomology of moduli spaces of smooth 2n-dimensional manifolds (or, equivalently, the classifying spaces of diffeomorphism groups of such manifolds). I will then give an example of how the theory may be used, by describing the result when the manifold in question is a hypersurface in CP^4.