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Speaker:

Cameron Rudd
Affiliation:

Urbana-Champaign
Date:

Mon, 16/05/2022 - 14:45 - 15:45
Parent event:

Arithmetic Groups and 3-Manifolds, May 16-20, 2022 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.

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