The Combinatorial Topology of Network Dynamics
Abstract: From food webs and internet router systems all the way to distributed algorithms, networks are ubiquitous in "nature". Analytical tools for the structure of networks and their dynamics span many different areas of mathematics, engineering, and computer science, leading to an array of challenging and fascinating mathematical problems. This talk contains an outline of an approach to the study of network dynamics, using new tools from combinatorial algebraic topology. The topological characteristics of certain combinatorial objects attached to a time series of network interactions carry qualitative information about system dynamics, including network performance.