Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification

该奖项将资助加拿大-墨西哥-美国表示理论、非交换代数和分类会议，该会议将于2022年6月在波士顿东北大学举行。表征理论是数学的一个分支，研究物理理论和数学对象的对称性。表征理论的主要对象往往只是更丰富的结构的影子，这些结构是通过更深入的研究而恢复的。非交换代数是数学的一个相关分支，研究量子理论、表示理论和几何中可交换对象的变形。会议的重点将是在表示理论和非交换代数的界面上的最新进展；为加拿大、墨西哥和美国在这些研究领域建立国际合作创造环境；让这三个国家的研究生、博士后和早期职业教师了解该领域的最新发展。一个海报环节将贯穿整个会议，早期职业参与者将展示他们的研究。加拿大-墨西哥-美国系列会议的第四次会议的主要科学主题将是表示论中的几何、代数和同调方法，非交换代数的表示论和同调性质，以及使用范畴方法研究这些问题。讲座将涵盖一些最新的趋势，包括：聚类代数，一元和加性范畴，量子对称，有限张量范畴，量子化仿射Kac-Moody代数的表示，Calabi-Yau代数和三角范畴，Hopfological代数，模表示理论的网络方法，heegard - flower同调的表示理论方面。有关会议的更多信息，请参阅https://yakimov.sites.northeastern.edu/can-mex-us-conf-2022/.This该奖项反映了NSF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。

The award will fund the Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification that will take place in Northeastern University, Boston in June 2022. Representation theory is a branch of mathematics that studies symmetries of physical theories and of mathematical objects. Often the main objects in representation theory are only the shadow of richer structures that are recovered through deeper study. Noncommutative algebra is a related branch of mathematics that studies deformations of commutative objects found in quantum theories, representation theory, and geometry. The foci of the conference will be on recent advances at the interface of representation theory and noncommutative algebra; on fostering an environment for the establishment of international collaborations between Canada, Mexico, and the USA in these research areas; and on exposing graduate students, post-docs, and early-career faculty in the three countries to current developments in the field. A poster session will run through the full meeting where earlier-career attendees will present their research.The main scientific topics for the fourth meeting in this series of Canada-Mexico-USA conferences will be geometric, algebraic, and homological methods in representation theory, representation theoretic and homological properties of noncommutative algebras, and the investigation of those problems using categorical methods. The talks will cover some of the most recent trends including: cluster algebras, monoidal and additive categorifications, quantum symmetries, finite tensor categories, representations of quantized affine Kac-Moody algebras, Calabi-Yau algebras and triangulated categories, Hopfological algebra, web approaches to modular representation theory, and representation theoretic aspects of Heegaard-Floer homology. For more information on the conference, see https://yakimov.sites.northeastern.edu/can-mex-us-conf-2022/.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.