Conference on Quantum Symmetries: Tensor Categories, Topological Quantum Field Theories, and Vertex Algebras

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Symmetry is all around us and, as such, forms a crucial tool to understand the natural world. Mathematicians have studied symmetries for hundreds of years and these classical results have guided almost every area of applied science. In the microscopic world, however, it is the counterintuitive rules of quantum science that must be obeyed. Scientists studying these phenomena therefore turn to a newly created field of mathematics known as quantum symmetry. While new, this field has already led to many breakthroughs and has played a crucial role in work that has been awarded several recent Fields medals and Nobel prizes. This project will bring together leading international experts and early career researchers from mathematics and physics to share techniques and advances in quantum symmetry. It will take place at the Centre de Recherches Mathématiques (CRM), Montreal, Canada, from October 10 to November 4, 2022, and will feature three weeks of lectures courses and a one-week international conference. For more information, see the conference website: http://www.crm.umontreal.ca/2022/Quantum22/index_e.phpThe topics of this event are important both in mathematics and physics. In mathematics, the latest developments in the representation theory of quantum groups at roots of unity bring new results to this well-developed subject. Related developments in topological quantum field theory (TQFT) and vertex algebras (VA) clarify the structure of "non-semisimple" TQFT and VA. Many recent conferences in these areas of research have focused on parts of these connections, but this conference will be unique in the sense that it will feature talks on each of the following topics: conformal field theories, vertex operator algebras, Hopf algebras and fusion categories, tensor categories in positive characteristic, constructions of modular categories, cohomological aspects of tensor categories, and more. These activities will connect communities working on different sides of the rich research area that is quantum symmetry. Other important aims include the training of the next generation of mathematical scientists and creating opportunities to meet with other researchers working on related problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.