Lie Groups, Representations and Discrete Mathematics

Ramanujan graphs are grphs with optimal bounds on their eigenvalues. They play an important role in combinatorics and computer science. Their constructions in the late 80's used the work of Deligne and Drinfeld proving the Ramanujan conjecture for GL(2) in char. 0 and p, resp. The work of Lafforgue enables starting to develope higher dimensional analogues.