Quantum symmetries and operator algebras

Theory of operator algebras grew out of attempts at providing a useful framework for quantum mechanics. While it has served its purpose, many connections to other fields of mathematics, such as ergodic theory, have been revealed, and from then on operator algebras lived their own life, not necessarily depending on the physical motivations.
Just like classical physics turned out to be insufficient for describing the world we live in, there are times where studying classical symmetries is not enough; quantum symmetries have to be taken into account. Interestingly, many early instances of quantum symmetries arise in problems of physical origin, such as the study of integrable systems.
Operator algebras and quantum symmetries have been always tightly connected and the project will be devoted to establishing new links between the two, in particular tackling open problems using previously unseen approaches. Especially exciting is the fact that recently there have been many applications of both operator algebras and quantum symmetries in the field of quantum information theory, which I will also pursue; I hope that developing these connections will have a tremendous impact on all the subjects involved.