# Lorentzian Geometry of Complex Networks

Tuesday, April 29, 2014 - 2:00pm - 2:50pm

Keller 3-180

Dima Krioukov (Northeastern University)

Random geometric graphs in Lorentzian spaces of constant positive curvature---de Sitter spaces---are shown to model well the structure and dynamics of some complex networks, such as the Internet, social and biological networks. Random geometric graphs on Lorentzian manifolds are known as causal sets in quantum gravity where they represent discretizations of the global causal structure of spacetime. If the expansion of a universe is accelerating, its spacetime is asymptotically de Sitter spacetime. Several connections between random de Sitter graphs, and Apollonian circle packings, Farey trees, divisibility network of natural numbers, and the Riemann hypothesis are also discussed.

MSC Code:

05C10

Keywords: