STOR Colloquium: Shankar Bhamidi (The University of North Carolina at Chapel Hill)

In the spirit of the Wednesday Colloquium this will be a non-technical introduction aimed at graduate students and the faculty about my research interests.  The last few years have seen an explosion in both empirical data on real world networks, as well as mathematical models to model these networks. These have inspired a plethora of interesting research questions in probability, statistics and operations research. Questions include trying to reconstruct real world networks in the presence of incomplete information, trying to simulate efficiently from various models of real word networks, as well as trying to understand properties of the network models proposed by practitioners. One can use powerful tools from probability theory, such as concentration inequalities, coupling techniques and stochastic process techniques to get a toe hold in analyzing these interesting questions. In this context I shall try to give a brief introduction to some of the following topics which have occupied a fair bit of my time over the last 2 years:

1.  Reconstructing multicast trees in computer science efficiently using powerful algorithms from phylogenetics (studying the tree of life).
2.  Methodology for analyzing Markov Chain algorithms used in social networks.
3. Spatially optimal networks.
4. Inhomogeneous Brownian motion and its intimate connections to components of random graphs.
5. Connection between the above theory of random graphs and models of coagulation in physics.
6. Random tree models and Brownian excursions.
7. Random matrix theory  and adjacency matrices of trees.

Refreshments will be served at 3:30pm in the 3rd floor lobby of Hanes Hall