Topics will vary from semester to semester. See Computer Science Division announcements.

Networks play a central role in our social and economic lives. They affect our well-being by influencing the information we receive, products we choose to buy, economic opportunities we enjoy, and diseases we catch from others. How do these networks form? Which network structures are likely to emerge in society? And how does the structure of the network impact the dynamics of the spread of an innovation or infection. This course tries to survey the mathematical results developed in the last few years on analyzing the structure of popular random networks, as well as the understanding of processes on them, with particular emphasis on epidemics. In addition it will touch on a recently very popular subject, the non-parametric modeling of a large graph via a graphon, and the related notion of graph limits. The course is loosely based on the text book “Random Graph Dynamics” by Rick Durrett, updated to what has happened since its publication, including the topics of graphons and graph limits, plus a larger emphasis on epidemics, as well as a short introduction to the topic of the spread of information and innovation. Additional literature, including original research papers, will be provided during the course. Tentative List of Topics Random Graph Models and Structure of Large Networks: Erdos-Renyi random graphs: cluster growth, formation of the giant connected component, diameter Models with community structure: Stochastic block model and topic models Scale-free graphs: random graphs with a fixed degree distribution, preferential attachment model and Polya urns Non-parametric models: graphons, graph limits, estimation, differential privacy on Networks Epidemics Models and their Behavior: Basic compartmental models (SIS, SIR, etc.) Differential Equation Approach: R0, exponential growth, size of an epidemic Mathematically rigorous derivation of Differential Equations from the underlying dynamic model Percolation and Oriented Percolation representation Analysis of contact inhomogeneities Algorithmic Aspects: Managing epidemics: algorithmic questions related to parameter estimation, testing, and contact tracing Viral spread of innovations in a social network: models of adoption of innovation, influence maximization, formation of social norms

Requisites

• Students not in the Master of Engineering Program

Repeat Rules