|
|
CMS Jeffery-Williams Lecture / Conférence Jeffery-Williams de la
SMC
- RAM MURTY, Department of Mathematics, Queen's University, Kingston,
Ontario K7L 3N6
Ramanujan graphs and zeta functions
-
In the last two decades, the theory of Ramanujan graphs has gained
prominence primarily for two reasons. First, from a practical
viewpoint, these graphs resolve an extremal problem in communication
network theory. Second, from a more aesthetic perspective, they fuse
diverse areas of mathematics, such as number theory, graph theory,
representation theory and algebraic geometry. This talk will survey
these developments. We will focus on the notion of a zeta function of
a graph and what the "Riemann hypothesis" means for the zeta
functions of regular graphs. We will also address the question of
explicit construction of Ramanujan graphs that involves the deeper
aspects of the theory of automorphic representations.
|
|
