Abstracts of plenary talks
Abstract: The cohomology of mapping class groups of surfaces (or moduli spaces of Riemann surfaces) has been studied intensively by different mathematical schools during the last 20 years. I will give a survey of recent results and the ideas behind them for the stable mapping class group, in particular the proof of Mumford's conjecture by Madsen and Weiss.
Abstract: Witt vectors are playing an important role in number theory and topology. Introduced by Witt in 1937, they were generalised by Cartier in 1967. But they remain mysterious objects with surprisingly many facets. We shall describe the Witt vector construction as a right adjoint to the forgetful functor from theta-rings to rings. Theta-rings were discovered by Bousfield in his work on the K-theory of H-spaces and independantly by the author. A characterisation of forgetful functors having a right adjoint was given by Wraith and Tall in 1970.
Abstract: One of the basic aims of modern differential geometry is to relate the curvature of a Riemannian manifold to its topology. In this lecture, I will discuss several different notions of curvature, and some differential-topological invariants of smooth compact 4-manifolds which arise from them. Amazingly enough, it turns out that different smooth structures on a fixed topological 4-manifold can often be distinguished from one another in terms of the curvature properties of the Riemannian metrics they support.