Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, May 3, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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30


Wednesday, May 3, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, May 3, 2017

#### Quantitative Mostow Rigidity: Relating volume to topology for hyperbolic 3-manifolds

###### Rosemary Guzman (UIUC)

Abstract: A celebrated result of Mostow states that if M, N are two closed, con- nected, orientable, hyperbolic n-manifolds which are homotopy equivalent in dimensions $n\geq 3$, then M, N are equivalent up to isometry. This unique geometric-topological relationship has been the framework for many important results in the field, including notable results providing lower bounds on the volume of M, and results relating volume to homology (Culler-Shalen). In this talk, we will focus on the case where the fundamental group of M has a property, $k-$free, for $k\geq5$, and discuss current work toward an improvement on the volume bound from the current known bound of 3.44 which holds for $k\geq 4$. This is joint work with Peter Shalen.