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# Colloquium – Professor David Gay (University of Georgia)

## March 9, 2022 @ 11:00 am - 12:00 pm

**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.