Expanders and Ramanujan graphs

Alex Lubotzky, Weizmann Institute, The Hebrew University, & Minerva Distinguished Visitor
Fine Hall Common Room

Expander graphs are of fundamental importance in computer science and in recent years, also in several areas of mathematics. A brilliant insight of Margulis showed their connection with representation theory (Kazhdan Property $T$) and paved the way to use the theory of automorphic forms to construct ``optimal" expanders (a.k.a. Ramanujan graphs) based on the work of Deligne and Drinfeld on the Ramanujan conjecture for $GL(2)$.