The goal of this talk is to both convey the importance of domain experts (like those involved in the current initiative) to guide mathematicians like me in their choice of problems, as well as convey the importance of math techniques in understanding proposed network models, through three personal research experiences:

1. In the context of one fundamental static model in social networks, the exponential random graph model (ERGMs) we will describe what math probability says in one specific (“ferromagnetic”) regime (joint work with Allan Sly and Guy Bresler).

2. In the context of change point detection for dynamic network models, we will describe the impact of hidden long-range dependence on the evolution of such models (Joint work with Sayan Banerjee, Iain Carmichael, Jimmy Jin, and Andrew Nobel).

3. In the context of attributed network models, we will describe what a theoretical analysis says about the behavior of centrality mechanisms such as page rank and degree centrality and the surprising efficacy of page rank-driven sampling in the specific setting of sampling from rare minorities (Joint work with Nelson Antunes, Sayan Banerjee, and Vladas Pipiras).”

Speaker: Shankar Bhamidi

Shankar Bhamidi works in both probability and statistics. In his research, he has worked on stochastic processes, and random networks including dynamics on network models and random graphs. He is interested in problems that have originated from some applied branch of science, to which probability can say something fruitful and non-trivial. He tries to find unifying mathematical principles which can be used to solve a variety of problems.