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

该NSF奖项支持参加国际会议“非交换代数和几何相互作用的最新进展和新方向”，该会议计划于2020年7月13日至17日在华盛顿大学西雅图分校举行。 预计将有来自世界各地的80-100名与会者参加。 数学是研究模式的。通常，这种模式是通过方程组来描述的。 多项式方程及其解在几乎所有科学领域都起着关键作用，如统计力学、基本粒子物理学、量子力学、机器人技术、晶体学和网络。通常，解决方案无法通过实验找到，并且通常它们不是数字而是函数（例如，微分算子或矩阵），因此，一般来说，它们不交换。非交换代数领域是寻求方法的科学，这些方法可以找到非交换变量中任何多项式方程系统的所有解，计划中的会议将重点关注最近在非交换代数中使用不同类型几何技术的研究活动。会议将包括调查讲座，研究讲座，海报会议，职业小组，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，以适应不同职业阶段的研究人员。10分钟的会谈和海报会议将在会议早期举行，以促进早期职业研究人员和高级研究人员在会议期间的最大讨论时间。资金将优先用于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。计划中的会议的目的是在非交换代数和相关领域产生新的研究，同时为非交换代数研究人员的发展做出贡献。这个主要的国际会议将涵盖非交换代数中当前活跃的几个主题，与组合学，几何学，数学物理学，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，特别是在非交换代数几何，Artin-Schelter正则代数，Calibi-Yau代数，Hopf代数和量子群，范畴理论和同调技术等领域。会议将汇集来自非交换代数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。 更多信息可以在会议网站上找到：https://sites.google.com/view/ndna2020/homeThis奖项反映了NSF的法定使命，并被认为值得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来支持。

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.