Conference: Facets of Noncommutative Geometry

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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.