Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Cameron Rudd
Affiliation:

Urbana-Champaign
Date:

Mon, 16/05/2022 - 14:45 - 15:45 Geodesic length and stable commutator length give geometric and topological notions of complexity for nullhomologous elements of the fundamental group of a hyperbolic manifold. The ratio of these complexity measures is a sort of geometric-topological isoperimetric ratio called the stable isoperimetric ratio. In this talk, I will discuss this ratio and describe how it relates to different aspects of the geometry and topology of hyperbolic manifolds. In particular, I will talk about how to control the size of this ratio and discuss a connection to the spectrum of the Hodge Laplacian acting on coexact 1-forms.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/11255