Abstract: "The Dirichlet–Ferguson process ζ is a random, purely discrete probability measure whose finite-dimensional distributions are Dirichlet distributions. 
It can be defined on a general state space and has numerous applications, such as in population genetics.
We shall present the fundamental chaos expansion by Peccati (2008), providing an explicit formula for the kernel functions. 
We proceed with developing a Malliavin calculus for ζ. To this end, we introduce a gradient, divergence and a generator which act as linear operators on ζ-measurable
random variables or random fields and which are linked by some basic formulas such as integration by parts.
While this calculus is motivated by Malliavin calculus for isonormal Gaussian processes and the general Poisson process, the strong dependence properties of ζ require
considerably more combinatorial efforts. We will identify our generator as the generator of the Fleming–Viot process and describe the associated Dirichlet form explicitly
in terms of the chaos expansion. If time permits, we shall also present a short direct proof of the Poincaré inequality.

The talk is based on joint work with Babette Picker (Karlsruhe)."