## EVENT DETAILS AND ABSTRACT

**Special Seminar**
**Title:** Rational Homology Spheres and Automorphic Forms

**Speaker:** Professor Frank Calegari

**Speaker Info:** Harvard University

**Brief Description:**

**Special Note**:

**Abstract:**

Let M be an irreducible compact connected 3-manifold.
A conjecture of Thurston predicts that whenever the fundamental
group of M is infinite the manifold M admits a finite cover with
non-trivial (rational) first homology. This conjecture implies
geometrization for such M, but is unknown even for hyperbolic
manifolds. Assuming M is hyperbolic, one possible approach to
Thurston's conjecture is to show that _any_ suitably large
(in some sense) manifold M must have non-trivial first homology.
In joint work with Nathan Dunfield we show that for a certain
natural definition of suitably large (large injectivity radius)
this approach fails. Our construction uses the Riemann Hypothesis.

**Date:** Friday, January 06, 2006

**Time:** 3pm

**Where:** Lunt 105

**Contact Person:** Prof. Matt Emerton

**Contact email:** emerton@math.northwestern.edu

**Contact Phone:** 847-491-3970

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