Graphs and Arithmetic

March 8 – 12, 2010
Organizers: W. Li (Penn State), E. Goren (McGill),
A. Granville (Montréal)

There is a long history of interaction between number theory and  combinatorics. In the past two decades, deep results in automorphic forms and number  theory were used to construct (optimal) expanders, which are known to have wide applications in computer science and communication networks. These techniques were generalized to construct higher dimensional analogues. In the meanwhile, zeta functions for graphs and complexes are better understood. Recent exciting developments in arithmetic combinatorics provide new tools to construct families of good expanders, and these expanders in turn are used to obtain deep number theoretic results. At the same time, the concept of expansion is extended in group theory and computer science to a different context.

In view of these fruitful developments, we think the time is ripe to hold a week long conference to review recent results in this area. Both theories and applications will be emphasized.