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\textsc{Seminar}
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\textit{Geodesics and Commensurability Classes of Arithmetic Hyperbolic 3-Manifolds (Part I)}
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Emily Hamilton\par
Emory University
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\textbf{Abstract:} This will be a two part lecture series. In the first lecture, we give an introduction to arithmetic Kleinian groups. In the second lecture, we show that if $M$ is an arithmetic hyperbolic $3$-manifold, then the set of all rational multiples of lengths of closed geodesics of $M$ both determines and is determined by the commensurability class of $M$. This implies that the spectrum of the Laplace operator of $M$ determines the commensurability class of $M$.\vspace{\fill}
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Monday, March 19, 2007, 1:00 pm\par
Mathematics and Science Center, E406
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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