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\textsc{Topology}
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\textsc{Seminar}
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\textit{Number Theory and a Lower Bound for Closed Geodesics, Part 2}
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Sean Thomas\par

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\textbf{Abstract:} Lehmer's conjecture (1933) states that the Mahler measure of an
algebraic number that is not a root of unity is bounded away from 1.
The aim of the seminar is to show the conjecture would imply there is a
positive lower bound for closed geodesics in compact arithmetic
hyperbolic 3-manifolds of finite volume. In the first lecture, I will
introduce the necessary background material on arithmetic hyperbolic
3-manifolds. Then, in the second lecture, I will show how Lehmer's
conjecture would imply the existence of the aforementioned positive
lower bound. Also, I will prove the existence of a positive lower bound
for closed geodesics in non-compact arithmetic hyperbolic 3-manifolds
of finite volume to fully address the topic.\vspace{\fill}
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Tuesday, February 10, 2009, 3:00 pm\par
Mathematics and Science Center: E406
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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