Operator Algebras and Quantum Physics: June 3-30, 2019

Organized by: Stefan Hollands, Vaughan Jones, Gandalf Lechner, Roberto Longo

Since Heisenberg’s and Jordan’s “matrix formulation” of quantum mechanics about one hundred years ago, theoretical quantum physics has been a major incentive for mathematical research into operator algebras. The stimulus from physics has helped the development of this field, founded by von Neumann with the motivation to clarify the mathematical structure of quantum mechanics. At the same time, theoretical quantum physics has benefited tremendously from new results in operator algebras, making the link between the two fields one of the most fruitful interdisciplinary research programs of the 20th and 21st century.

Nowadays, both the quantum physics and operator algebras groups have grown into large and diverse communities with many subareas and new links to other fields. For example, in the last decades, we have witnessed connections between operator algebras and knot theory, free probability, K-theory, and further topics. In quantum physics, the most active fields that have a close link to operator algebras are quantum field theory and quantum statistical mechanics. More recently, also connections between quantum information theory and operator algebras began to emerge.

Despite its enormous phenomenological success, quantum field theory still contains many challenging open questions, for example regarding its proper place within mathematics in general, as well as the mathematical status of various field theoretic models, including in particular the types of models quantitatively describing the interactions of elementary particles. It is widely expected that new mathematical insights are needed in order to make further progress on these fronts.

The aim of this program is to bring together established experts and young researchers in these fields, focusing on operator-algebraic approaches to quantum field theory, subfactor theory, and quantum information theory.

There will also be a workshop associated with this program: Operator Algebras and Applications from June 17-21, 2019.