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

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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.