Dynamics on Networks

This workshop will bring together researchers from different disciplines to exchange ideas stemming from diverse perspectives on dynamics on networks.   The focus of the workshop can be summarized in terms of a central construction:  Consider a collection of elements, individuals – more generally, nodes – that can each take on one of several states at any given time.  Suppose that nodes interact in a way that (a) depends on their states and their connections, and (b) may cause their states to change.  In this setting, a wide range of questions arise that span topics in combinatorics, network and graph theory, probability theory, and dynamical systems, with applications in fields such as sociology, epidemiology, and neuroscience.  These questions include issues of global architecture, such as how the eventual pattern of states across an interacting network of nodes depends on the overall network structure; issues of local initialization, such as what properties of local subsets of nodes can allow them to strongly influence the rest of the network; and issues of dynamics, relating to how the set of available states and the rules for transitioning between them affect pattern formation in the network.  By promoting interaction of researchers who have disparate perspectives and expertise relevant to aspects of this general problem class, this workshop will fertilize new collaborations and progress on questions of interest to a range of communities.