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

对称无处不在，因此，对称是理解自然世界的重要工具。数学家们研究对称性已经有几百年了，这些经典的结果几乎指导了应用科学的每个领域。然而，在微观世界中，必须遵守的是量子科学的反直觉规则。因此，研究这些现象的科学家转向了一个新创建的数学领域——量子对称。虽然这是一个新领域，但它已经带来了许多突破，并在最近几次获得菲尔兹奖和诺贝尔奖的工作中发挥了关键作用。该项目将汇集顶尖的国际专家和来自数学和物理学的早期职业研究人员，分享量子对称的技术和进展。该课程将于2022年10月10日至11月4日在加拿大蒙特利尔的数学<s:1>研究中心（CRM）举行，包括为期三周的讲座课程和为期一周的国际会议。欲了解更多信息，请参阅会议网站：http://www.crm.umontreal.ca/2022/Quantum22/index_e.phpThe本次活动的主题在数学和物理中都很重要。在数学方面，统一根量子群表示理论的最新发展为这一发展良好的学科带来了新的成果。拓扑量子场论（TQFT）和顶点代数（VA）的相关发展阐明了“非半简单”TQFT和VA的结构。最近在这些研究领域的许多会议都集中在这些连接的部分上，但这次会议将是独一无二的，它将以以下主题为特色：共形场论，顶点算子代数，Hopf代数与融合范畴，正特征张量范畴，模范畴的构造，张量范畴的上同调方面，等等。这些活动将把在量子对称这个丰富的研究领域的不同方面工作的社区联系起来。其他重要目标包括培训下一代数学科学家，并创造机会与其他研究相关问题的研究人员会面。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.