Generating functionals on quantum groups

We will discuss generating functionals on locally compact
quantum groups. One type of examples comes from probability: the family
of distributions of a L\'evy process form a convolution semigroup,
which in turn admits a natural generating functional. Another type
of examples comes from (locally compact) group theory, involving semigroups
of positive-definite functions and conditionally negative-definite
functions, which provide important information about the group's geometry.
We will explain how these notions are related and how all this extends
to the quantum world; see how generating functionals may be (re)constructed
and study their domains; and indicate how our results can be used
to study cocycles. Based on joint work with Adam Skalski.