Speaker: Hokuto Konno

Title: The diffeomorphism and homeomorphism groups of K3

Abstract:
K3 surfaces are one of the most important classes of complex
surfaces. In this talk, I will explain the following two results on the
diffeomorphism and homeomorphism groups of a K3 surface, which are
proven using gauge theory. A significance of these results is that it
turned out that a K3 surface gives the first answers in dimension 4 to
questions which are formulated for an arbitrary manifold. The first
result is that a K3 surface gives the first counter example to the
Nielsen realization problem in dimension 4, which asks if there is a
lift of an arbitrary finite subgroup of the mapping class group to the
diffeomorphism group. The second result is that the natural map from the
fundamental group of the diffeomorphism group of a K3 surface to that of
the homeomorphism group is not surjective. This gives the first example
of a 4-manifold satisfying such a property. This is joint work with
David Baraglia.