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.