### PROBQUANTUMGROUPS

**Probability and Quantum Groups**

Individual Intra-European Fellowship (Marie Curie Fellowship) of
Adam
Skalski,

1st October 2010 - 30th September
2012.

The project lies at the intersection of functional analysis,
probability theory and quantum algebra, with possible applications to
mathematical physics. It is broadly concerned with the analysis of
evolutions of systems related to quantum groups, using the language of
noncommutative probability. The latter, which extends the classical
stochastic theory, is necessary to describe random phenomena
encountered in the microscopic world. A specific goal is the
mathematically rigorous investigation of probabilistic aspects of both
local and long-time behaviour of systems in the presence of quantum
symmetry, represented by quantum groups. Recent years have brought a
dynamic development of both general theory and concrete examples of
quantum groups and, more generally, quantum spaces. It is natural to
expect that stochastic methods and interpretations will be
indispensable to deepen the understanding of both discrete and
continuous dynamical systems arising in this context. Connections with
noncommutative geometry are also expected to be uncovered, thus
extending the longstanding fruitful interaction between classical
probability, geometry and algebraic structures.

Seventh Framework Programme (FP7)
Marie-Curie Actions