Conference: Facets of Noncommutative Geometry

该奖项为定于2022年6月11日至12日在伊利诺伊大学香槟分校举行的题为《非对易几何的方面》的会议提供支持。这次会议的目的是将一群拥有专业知识的数学家聚集在一起，他们围绕着扩展的几何概念。研究这些几何的两个主要动力来源是量子物理中的海森伯格测不准原理和数学中的抽象代数。这次会议将为两个截然不同的研究小组提供一个环境，让他们走到一起，交流思想，了解最近的发展。会议的一个中心目的是为早期的数学家提供一个视角和进入这个令人兴奋和快速发展的领域的切入点。非对易几何是一种普遍的观点，在没有直接的谱解释的情况下，人们试图将工具、透视和直觉从几何应用到非对易代数结构中。这一观点在表象理论、张量范畴、辛几何和量子场论等许多领域都取得了丰硕的成果，但在不同的群体之间往往没有直接的交流。会议将包括与会者，他们可以阐明这一重要主题的不同方面。这次会议旨在为交流意见和评估整个实地的状况提供一个独特的机会。这次聚会的目的是将早期职业研究人员(主要是研究生、博士后和早期教师)聚集在一起，向他们介绍广阔的视野，并为形成新的联系和合作提供机会。将注意多样性，不仅在申请过程中，而且在为参与者提供资金和为传统上代表人数不足的群体创造一个欢迎的环境方面。会议将重点突出最近的发展，以激励下一代非对易几何仪。有关会议的更多信息，请参见https://publish.illinois.edu/facets-ncg-conf2022/.This奖项，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 award provides support for a conference entitled "Facets of Noncommutative Geometry," scheduled for June 11-12, 2022 at the University of Illinois at Urbana-Champaign. The conference aims to bring together a group of mathematicians with expertise centered around an expanded notion of geometry. Two of the main sources of motivation for investigating these geometries are the Heisenberg uncertainty principle in quantum physics and abstract algebra in mathematics. The conference will provide a setting for two largely distinct groups of researchers to come together, exchange ideas, and learn about recent developments. A central aim of the conference is to provide early-career mathematicians perspective and an entry point into this exciting and fast-moving field.Noncommutative geometry is a general viewpoint in which one seeks to apply tools, perspectives, and intuition from geometry to noncommutative algebraic structures in the absence of a direct spectral interpretation as rings of functions. This viewpoint has been extremely fruitful in many settings, including representation theory, tensor categories, symplectic geometry, and quantum field theory, often without direct communication between the various groups. The conference will include participants who can illuminate different aspects of this overarching theme. The meeting is designed to provide a unique opportunity for an exchange of ideas and a stock-taking on the state of the field as a whole. The gathering is aimed at bringing together early-career researchers, primarily graduate students, postdocs and early-stage faculty, and introducing them to a broad vision and providing opportunities for forming new connections and collaborations. Attention will be paid to diversity, not only in the application process, but also in the funding of participants and creating a welcoming environment for traditionally underrepresented groups. The conference will focus on highlighting recent developments to inspire the next generation of noncommutative geometers. For more on the conference, see https://publish.illinois.edu/facets-ncg-conf2022/.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.