Conference: Seattle Noncommutative Algebra Conference

This award supports participation in the "Seattle Noncommutative Algebra Conference" that will take place December 15-19, 2025 at the University of Washington in Seattle. Noncommutative algebra is the study of algebraic structures in which the commutative law of multiplication does not hold, that is, multiplying x by y may yield a different result than multiplying y by x. This framework is particularly effective in the study of symmetry, quantum phenomena, geometry and more. The conference will bring together researchers from across these areas, along with graduate students and early-career researchers, to survey current progress, highlight open problems, and foster new collaborations and directions for future research. Activities will include expository and research lectures, student presentations, problem sessions, and discussions on computational techniques. The conference aims to stimulate progress on key structural questions in the field and build bridges between a broad range of noncommutative perspectives across mathematics. In more detail, the five-day conference will focus on several active research programs in noncommutative algebra, with connections to representation theory, algebraic geometry, Poisson algebra and Poisson geometry, quantum groups, category theory, topology, and combinatorics. A central theme is noncommutative projective geometry, with particular emphasis on two major classification problems: (i) the classification of Artin-Schelter regular algebras of global dimension four, which geometrically correspond to three-dimensional quantum projective spaces; and (ii) Artin's conjecture on division algebras of transcendence degree two, which seeks a birational classification of noncommutative projective surfaces. Additional topics include Calabi-Yau algebras, noncommutative invariant theory, and emerging methods in computational algebra. The conference website is https://sites.google.com/uw.edu/seattlencalgebra2025. 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.