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# An Introduction to Nielsen Fixed Point Theory

by

Evelyn Hart
Colgate University

February 20, 2006
4:30 pm
Bailey Hall 201

Pastries and drinks will be served at 4 pm in Bailey 204

## Abstract:

Students don't know what that title means unless they have already seen the talk. This is often true for talks in mathematics. So the abstract helps students to decide whether to attend the talk. But the abstract often uses words that will be defined during the talk and thus are mysterious. What is a student to do? This talk requires no mathematical background. There will be at least one joke and also instruction on how to perform a bit of magic at the blackboard. In addition, you will see how basic ideas of topology and group theory are applied to Nielsen fixed point theory. (If you've never heard of topology and group theory, that's fine.) Here is a rough description of Nielsen fixed point theory. Suppose that f is a continuous function sending points on the surface of a doughnut to other points on the surface of the doughnut. A fixed point of f is a point that is sent to itself. It is important in the theories of dynamical systems and differential equations to be able to find the number of such fixed points. But instead of studying only f, we must consider functions that are similar to f in a certain way. We care about functions that are continuous deformations of f. In fact, our goal is to estimate the smallest number of fixed points when we compare all of the continuous deformations of f. (When you come to the talk you will find out what all of this means. See you there!)

For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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