Math 693b: Graphs, Spectral Theory, and Modular Forms

Stephen D. Miller

This Course is Independent of Last Semesters Course

Summary: This semester I want to begin by discussing the Selberg Property Tau as well as his "1/4" Eigenvalue Conjecture.  This will involve some graph theory.  We will consider certain expander graphs constructed by A. Terras et al and eventually derive Tau from them, resulting in further applications to graphs.  We will do a study of harmonic analysis on SL(2,Z)\SL(2,R), including the trace formula.  Other possible topics include
 Stephen Miller, Dec 7, 2000.