3:00–4:00 pm Eckhart Hall, Room 202
Title: Towards a Nielsen/Thurston program for K3 manifolds.
Abstract: In the 1970s Thurston showed how to best represent a mapping class of a closed surface by a diffeomorphism (a mapping class of a manifold is just an isotopy class of self-diffeomorphisms of that manifold; these make up a group under composition). Kerckhoff proved around 1980 that a finite group of mapping classes of a closed surface can be realized by a group of diffeomorphisms of that surface, thus answering an old question (1932) of Nielsen.
After a (very) brief review of the above, I will report on joint work with Benson Farb which addresses these questions for a particular kind of 4-manifold, namely one that is diffeomorphic to a (complex) K3 surface.