Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry

这一NSF奖支持参加计划于2020年7月13日至17日在华盛顿州西雅图的华盛顿大学举行的国际会议`非对易代数和几何相互作用的最新进展和新方向‘’。预计将有来自世界各地的80-100人参加。数学是对模式的研究。通常，这种模式是通过方程系统来描述的。多项式形式的方程组及其解在统计力学、基本粒子物理、量子力学、机器人学、结晶学和网络等几乎每一个科学领域都扮演着重要的角色。通常，解决方案不能通过实验找到，而且通常它们不是数字，而是函数(例如，微分运算符或矩阵)，因此，通常它们不交换。非对易代数领域是寻找方法背后的科学，这些方法可以在非对易变量中找到任何多项式式方程组的所有解，计划中的会议将集中于最近的研究活动，这些研究活动使用了非对易代数中不同类型的几何技术。会议将包括调查演讲、研究演讲、海报会议、职业小组讨论、公开讲座和研究讨论。研究讲座将包括50分钟、25分钟和10分钟的讲座，以适应处于不同职业阶段的研究人员。10分钟的演讲和海报会议将在会议早期进行，以便在会议期间促进早期研究人员和高级研究人员之间的最大讨论时间。将优先为初级参与者和来自传统上在数学科学中代表性不足的群体的研究人员提供资金。计划中的会议的目的是在非对易代数及其相关领域产生新的研究，同时促进非对易代数研究队伍的发展。这次重要的国际会议将涵盖当前活跃在非对易代数中的几个主题，与组合学、几何学、数学物理、数论和拓扑学有着广泛的联系。它将强调最近令人兴奋的发展和新兴的未来方向，特别是在非对易代数几何、Artin-Schelter正则代数、Calibi-Yau代数、Hopf代数和量子群、范畴理论和同调技巧等领域。会议将汇聚非对易代数领域不同专业的顶尖专家，鼓励与会者从广泛的角度和方法进行互动。更多信息可在会议网站上找到：https://sites.google.com/view/ndna2020/homeThis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智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This NSF award supports participation in the international conference ``Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry,'' which is planned for July 13–17, 2020, at the University of Washington in Seattle, Washington. It is expected that 80–100 participants from all over the world will attend. Mathematics is the study of patterns. Frequently, such patterns are described via systems of equations. Systems of polynomial-style equations and their solutions play a critical role in almost every scientific field, such as statistical mechanics, elementary particle physics, quantum mechanics, robotics, crystallography, and networking. Often, the solutions cannot be found by experimentation, and often they are not numbers but are functions (e.g., differential operators or matrices), and so, in general, they do not commute. The field of noncommutative algebra is the science behind seeking methods that find all solutions to any system of polynomial-style equations in noncommuting variables, and the planned conference will focus on recent research activities that use different types of geometric techniques in noncommutative algebra. The conference will consist of survey talks, research talks, a poster session, a career panel, a public lecture, and research discussions. The research talks will feature 50-minute, 25-minute, and 10-minute lectures in order to accommodate researchers at various career stages. The 10-minute talks and poster session will take place early in the conference in order to facilitate maximal discussion time during the conference between early-career researchers and senior researchers. Funding will be prioritized for junior participants and for researchers from groups that are traditionally under-represented in the mathematical sciences.The purpose of the planned conference is to generate new research in noncommutative algebra and related areas, while contributing to the development of the research workforce in noncommutative algebra. This major international conference will cover several topics of active current interest in noncommutative algebra, with broad connections to combinatorics, geometry, mathematical physics, number theory, and topology. It will emphasize recent exciting developments and emerging future directions, particularly in such areas as noncommutative algebraic geometry, Artin-Schelter regular algebras, Calibi-Yau algebras, Hopf algebras and quantum groups, category theory, and homological techniques. The conference will bring together the leading experts from different specialties within noncommutative algebra, encouraging interactions between participants from a broad range of perspectives and approaches. Further information can be found at the conference website: https://sites.google.com/view/ndna2020/homeThis 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.