## Geometry and Dynamics

Andy Hammerlindl (Monash)

Abstract

Consider a function from the circle to itself such that the derivative is greater than one at every point. Examples are maps of the form $$f(x) = mx$$ for integers $$m > 1$$. In some sense, these are the only possible examples. This fact and the corresponding question for maps on higher dimensional manifolds was a major motivation for Gromov to develop pioneering results in the field of geometric group theory.

In this talk, I'll give an overview of this and other results relating dynamical systems to the geometry of the manifolds on which they act and (time permitting) talk about my own work in the area.

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