EVENT DETAILS AND ABSTRACT

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.