Title: Branching Processes, Random Trees and Superprocesses

We present some recent developments concerning the genealogy of branching processes, and their applications to superprocesses. We also discuss connections with partial differential equations, statistical mechanics and interacting particle systems.

1991 Mathematics Subject Classification: 60J80,60G57,60K35,35J60

Keywords and Phrases: Branching processs, random tree, superprocess, semilinear partial differential equation, L\'evy process, voter model, lattice tree.

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