Analysis, Spectra and Number Theory, a Conference in Honor of Peter Sarnak’s 61st Birthday

Ramanujan graphs has been defined and constructed in the 80's by Lubotzky-Phillips-Sarnak and by Margulis. In recent years a high dimensional theory of expanders is emerging and in particular Ramanujan complexes. In the talk we will present a joint work with T. Kaufman and D. Kazhdan in which the Ramanujan complexes are used to construct simplical complexes of bounded degree with the topological overlapping property. This answers a question of Gromov.