**Refreshments will be served at 10:30 a.m. in 301 GP**
The presentation will begin at 11:00 a.m. in 346 Gordon Palmer Hall

Title: Smooth automorphisms of the 4‐dimensional sphere

Abstract: This is a talk about smooth 4‐dimensional topology, in which the
objects are smooth 4‐manifolds (spaces locally like R^4 equipped with the
ability to do calculus), and the morphisms are differentiable maps. The
simplest closed smooth 4‐manifold is S^4, the 4‐dimensional unit sphere in
R^5. Often the focus in this field is on classifying the objects; for example, the
smooth 4‐dimensional Poincare conjecture is that every closed smooth 4‐
manifold homotopy equivalent to S^4 is diffeomorphic (smoothly isomorphic)
to S^4. An equally important project is to classify, in an appropriate sense, the
automorphisms of given objects; it turns out that even the automorphisms of
S^4 are poorly understood. I will discuss this problem, some recent results of
myself and others, and hopefully leave you at least with a sense that one
might be able to “draw pictures” of automorphisms of S^4 and make
reasonably combinatorial arguments about them.