Susquehanna Mathematics Colloquium

Wednesday, March 23d

Michael McCooey Franklin and Marshall College

Topological symmetries of spheres

ABSTRACT: We will begin by trying to understand what a higher-dimensional "sphere" is, from a mathematical point of view.

We'll look at some examples of symmetries of spheres from linear algebra and determine what crucial features they have in common, then use these as a jumping-off point to discuss topological symmetries. (Linear algebra symmetries are rigid, while topological ones may be "floppy" and "stretchy".) Along the way we will use the Intermediate Value Theorem from calculus to understand fixed points of symmetries, and investigate the connection between the fixed points of symmetries and knot theory. Strange and wonderful things begin to happen in dimension four...

Most of the talk should be accessible to students who have taken linear algebra and have some geometrical intuition. Faculty should enjoy and learn from it as well.

Talks begin at 4:15 in Seibert 017. Refreshments at 4:00.