The investigator studies influences of boolean functions using Gaussian Hilbert spaces. The investigator is interested in particular in problems arising in the theory of social choice, in hardness of approximation and in learning theory. The investigator further studies a number of inference algorithms on graphical models using techniques from probability and statistical physics in general and the theory of Gibbs measures on trees in particular. These algorithms are used for phylogenetic inference, for computing marginals in Markov random fields and for solving satisfiability problems.
In the first topic the investigator studies questions like: ``How do we design a reliable voting scheme? What is the effect of error in voting machines on the outcome of a vote?''. The same mathematical questions are also important in understanding theoretical questions arising in high-performance computing, in particular the existence of efficient algorithms for approximately solving ``hard'' problems. In the second topic, the investigator is motivated by questions on ancestral relationship that are central in modern biological and medical research, and in problems of high-dimensional statistical inference that play an important role in expert systems and data-mining.
