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large random combinatorial structures, random matrices, superprocesses & other measure-valued processes, probability on algebraic structures -particularly local fields, applications of stochastic processes to biodemography, mathematical finance, population genetics, phylogenetics & historical linguistics

probability theory, statistical mechanics

integrable probability, random matrices, asymptotic representation theory

theoretical computer science, random matrices, geometry of polynomials

operator algebras, free probability theory, random matrices, K-theory of operator algebras, single operator theory