Monday December 4th at 4.30pm

neighbors. The terminology and non-trivial constructions originate in the theory of modular forms, which is part of number theory. After some

background material I shall attempt to describe two constructions, due to Lubotzky-Philips-Sarnak and Pizer and explain how the relation to

modular forms comes about. I shall then discuss joint work with Dennis Charles and Kristin Lauter (both at Microsoft Research) that constructs

hash functions from Ramanujan graphs and explain some (seemingly) new questions it raises.