Discrete groups, expanding graphs and invariant measures

Expanding Graphs.- The Banach-Ruziewicz Problem.- Kazhdan Property (T) and its Applications.- The Laplacian and its Eigenvalues.- The Representation Theory of PGL 2.- Spectral Decomposition of L 2(G(?)\G(A)).- Banach-Ruziewicz Problem for n = 2, 3 Ramanujan Graphs.- Some More Discrete Mathematics.- Distributing Points on the Sphere.- Open Problems.