Hodge Theory for Poisson Varieties and Nonperturbative Quantization

Explore a lecture on Hodge theory for Poisson varieties and nonperturbative quantization presented by Brent Pym from McGill University. Delve into Kontsevich's deformation quantization formula and its application to Poisson manifolds, examining the challenges posed by its Feynman-style series expansion. Discover how K-theory and mixed Hodge structures can be utilized to construct natural "period coordinates" on the moduli space of smooth Poisson varieties, enabling simpler and explicit nonperturbative computations. Gain insights into the conceptual explanation for the appearance of classical transcendental functions in relations defining well-known noncommutative algebras. Learn about the forthcoming joint work with A. Lindberg that forms the basis of this one-hour and three-minute talk hosted by the University of Miami.

Brent Pym, McGill University: Hodge theory for Poisson varieties and nonperturbative quantization