DATE                    TOPICS                                       SUGGESTED READING               9/2, 9/5 Introduction, Overview Hyperbolic Geometry Chap. 2.1 9/9, 9/12 Fundamental Domains, Lattices Chap 2.2 9/16, 9/19 Gauss-Bonnet, Lattices are Geometrically Finite Chap 2.2 9/23 NO CLASS 9/26 Cusps, parabolic/unipotent elements Structure of Dirichlet Domain Chap 2.2 9/30, 10/3 Ergodicity, Recurrence Chap 1.1 10/7, 10/10 Mean Ergodic Theorems Chap 1.2 10/14, 10/17 Mixing Chap 1.2 10/21, 10/24 Unique Ergodicity Benford's Law 3x+1 Map, zeta(1/2+it) Chap 1.3 Benford's Law, values of L-functions and the 3x+1 Problem 10/28 NO CLASS 10/31 Equidistribution Weyl's Criterion Chap 1.3 11/4, 11/7 Unit Tangent Bundle Geodesic/Horocycle Flow Chap 2.3 11/11, 11/14 Howe-Moore Chap 3.1 11/18, 11/21 Equidistribution of Spheres Lattice Point Counting Chap 3.3 Wed 11/26 Horocycle Flow Zagier/Sarnak Chap 4.1-4.4 12/5 NO CLASS 12/2 Bounds for Fourier Coefficients Sparse Equidistribution 12/9 Overview