# Rational Homology Spheres and Automorphic Forms

 IAS/PRINCETON NUMBER THEORY SEMINAR Topic: Rational Homology Spheres and Automorphic Forms Speaker: Frank Calegari Affiliation: Harvard University Date: Wednesday, November 2 Time/Room: 2:00pm - 3:00pm/Fine Hall 314

Let K be an imaginary quadratic field. Modular forms for K are related to the cohomology of arithmetic 3-manifolds. By using the Galois representations associated to such forms we produce an explicit tower of rational homology three spheres with certain properties, answering a question of Cooper. Along the way we give the world's most complicated proof that the modular curve X_0(1) has genus zero. (Joint work with Nathan Dunfield)