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Chinese history (Tang, Song, Liao dynasties), global middle ages, sino-steppe relations, aristocracies, meritocracy, elites, political culture, death ritual, premodern cities, premodern empires, imperialism, ethnicity, nationalism, national identity, social networks, frontiers, boundaries and borderlands, digital methodologies

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