This conference is focused on three closely related subjects: groups and their actions in geometry and topology, operator algebras, and integrable systems. These branches of mathematics are important in themselves and have wide applications in various areas. Geometric ideas and methods play a crucial role in interconnection and development of these fields. Integrability and other properties of dynamical systems are often related with geometry and symmetries of these systems, i.e., group actions. Many operator algebras are produced from groups and bear group action, so that properties of these algebras reflect properties of the corresponding groups and vice versa. Quantum mechanics and modern physical theories use operator algebras as a basic tool. There are many other similar examples of mutual interference of these fields.

The main purpose of the conference is to bring together experts in the major fields listed in its title, in order to disseminate important ideas and broaden the areas of mutual interest.