Research

My research interests include stochastic graph theory and network modeling, applications of probabilistic methods to combinatorial problems, extremal combinatorics, graph coloring, and random matrices. A list of publications can be found on my CV.

Among other things, I am currently researching various properties of the Stochastic Kronecker Graph model (see, for example, Kronecker Graphs: An approach to modeling networks by J. Leskovec, D. Chakrabarti, J. Kleinberg, C. Faloutsos, and Z. Ghahramani). In particular, I am exploring spectral properties of the model, as well as thresholds for various graph properties. I am also interested in generalizations of this model, such as the Multiplicative Attribute Graph.

Motivated by interesting ideas in the Kronecker Graph model, I am also working on mathematical properties of the Waxman Model. Despite widespread use in biological and electrical engineering related problems, the Waxman Model has been overlooked by the mathematical community. There is little mathematical research available regarding the structure of the graph, or important graph properties.

In addition, I am exploring applications of matrix concentration inequalities to random graphs (see, for example, On the Spectra of General Random Graphs by F. Chung and M. Radcliffe). Concentration inequalities play an important role in the study of random variables, and the use of such inequalities to study properties of random matrices, and in particular spectral structure, seems to be a promising tool.

Last updated: 13 July 2013