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

对称性就在我们身边，因此，它是理解自然世界的重要工具。数学家们已经研究对称性几百年了，这些经典的结果几乎指导了应用科学的每一个领域。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们转向了一个新创建的数学领域，称为量子对称性。虽然是新的，但这个领域已经取得了许多突破，并在最近获得几项菲尔兹奖和诺贝尔奖的工作中发挥了关键作用。该项目将汇集来自数学和物理的国际领先专家和早期职业研究人员，分享量子对称性的技术和进展。它将于2022年10月10日至11月4日在加拿大蒙特利尔的Centre de Recherches Mathématiques（CRM）举行，并将举办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本次活动的主题是重要的数学和物理。在数学中，量子群在单位根上的表示理论的最新发展为这个发展良好的学科带来了新的结果。拓扑量子场论（TQFT）和顶点代数（VA）的相关发展阐明了“非半单”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一部分，但这次会议将是独一无二的，因为它将在以下每个主题上进行专题演讲：共形场论，顶点算子代数，霍普夫代数和融合范畴，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。 这些活动将连接在量子对称性这一丰富研究领域的不同方面工作的社区。其他重要的目标包括培养下一代数学科学家，并创造机会与其他研究人员在相关问题上的工作。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.