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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

physics, theoretical condensed matter, topological phase transitions, high-temperature superconductivity, organization principles enabling microscopic degrees of freedom to behave cooperatively, matter and their formation mechanisms, low dimensional quantum magnets, strongly correlated Fermi and Bose fluids