Discrete Groups, Expanding Graphs and Invariant Measures

1. Expanding Graphs
Alexander Lubotzky

2. The Banach-Ruziewicz Problem
Alexander Lubotzky

3. Kazhdan Property (T) and its Applications
Alexander Lubotzky

4. The Laplacian and its Eigenvalues
Alexander Lubotzky

5. The representation theory of PGL2
Alexander Lubotzky

6. Spectral Decomposition of
L^2 (G(mathbb{Q})backslash G(mathbb{A}))

Alexander Lubotzky

7. Banach-Ruziewicz Problem for n=2, 3; Ramanujan graphs
Alexander Lubotzky

8. Some More Discrete Mathematics
Alexander Lubotzky

9. Distributing Points on the Sphere
Alexander Lubotzky

10. Open Problems
Alexander Lubotzky

Keywords: Mathematics, Group Theory and Generalizations, Real Functions, Number Theory, Differential Geometry