Emmy-Noether-Seminar: Deformation Quantization via Categorical Factorization Homology

Deformation Quantization via Categorical Factorization Homology

Lukas Müller (Perimeter)

Abstract: Factorization homology `integrates‘ (higher) categorical structures, such as representation categories of Hopf algebras, VOAs, or quantum groups, over manifolds. In my talk, I will discuss an approach for constructing local-to-global deformation quantizations of symplectic manifolds, such as moduli spaces of flat bundles (character varieties), based on factorization homology. In this approach, local quantizations are governed by E_2​-deformations of symmetric monoidal categories, which, when integrated over 2-dimensional manifolds, lead to Poisson structures and deformation quantizations. Applying the general framework to the Drinfeld category reproduces deformations previously introduced by Li-Bland and Ševera. As a direct consequence, we can conclude a precise relation between their quantization and those introduced by Alekseev, Grosse, and Schomerus. No prior knowledge of factorization homology will be assumed. The talk is based on joint work with Eilind Karlsson, Corina Keller, and Ján Pulmann.