My research interests lie mainly in combinatorics and graph theory, and in related areas of probability, algorithms and statistical physics. I spend much of my time thinking about graphs and networks and other discrete structures, both from a structural and from a probabilistic perspective.
A particular interest in the last few years has been the connection between local structure and global structure. For example, given some local information about a graph or network, when does that tell us something about the global structure? Conversely, given some large-scale structural information about a network, when is that reflected in the local structure? And what about algorithms? Does it get much easier to solve a global problem if we know how to solve it locally? Does the problem get much simpler if we consider a random network?