Brent PYM

Title: Geometry and quantization of Poisson Fano manifolds

Abstract: Complex Poisson manifolds and the noncommutative algebras that "quantize" them appear in many parts of mathematics, but their structure and classification remain quite mysterious, especially in the positively curved case of Fano manifolds.  I will survey recent breakthroughs on several foundational conjectures in this area, which were formulated by Artin, Bondal, Kontsevich and others in the 80s and 90s.  For instance, we will see that the curvature of a Poisson manifold has a strong effect on the singularities of its associated foliation, and that the remarkable transcendental numbers known as multiple zeta values arise naturally as universal constants in the corresponding quantum algebras.