Vadim Vologodski (University of Toronto)
Title: Fedosov quantization in positive and mixed characteristic.
Abstract: Fedosov and, independently, de Wilde and Lecomte proved that every smooth symplectic manifold admits a distinguished deformation quantization defined up to a noncanonical isomorphism.
Bezrukavnikov and Kaledin later established an analogous result for affine symplectic varieties over a field of characteristic zero.
Moreover, the assignment that takes an affine symplectic variety to the category of modules over the quantized algebra can be promoted to a functor from the category of all symplectic varieties to the 2-groupoid of categories.
I will review some of these results and then explain an analogous picture in positive characteristic (due to Bezrukavnikov-Kaledin and Bogdanova-Kubrak-Travkin-Vologodsky). A new feature in characteristic p is that the categorical quantization is defined over a mod-p analogue of the twistor line rather than merely over a formal disk.
If time permits, I will also discuss a construction, due to Travkin, of the canonical categorical quantization over the ring of integers.
Location: UQAM PK-5675
or online: