Prof. Dr. Moritz Weber, Universität des Saarlandes

Since the early days of the foundation of quantum mechanics, 100 years ago, it was clear that a new kind of mathematics was needed in order to capture the new physics. At that time, John von Neumann formulated his principles of quantum mechanics and one of the main features was noncommutativity - the fact, that two observables A and B need not to commute. This was the starting point of a systematic study of noncommuting operators which quickly emancipated from „just a physics tool“ to an own branch in mathematics as such. More and more often, it is called quantum mathematics nowadays and it comprises C*-algebras (aka quantum topology), von Neumann algebras (aka quantum measure theory), Connes’s noncommutative geometry (aka quantum differential geometry), quantum groups and many more.
I will give a brief survey on quantum mathematics, and I will then focus on an introduction to quantum symmetries and their link to quantum information theory. I aim to speak to mathematicians, physicists and computer scientists at the same time.