From geometric quantization to noncommutative algebraic geometry

Abstract: The usual homogeneous coordinate rings studied in algebraic geometry may be obtained from quantization of the integer multiples of a symplectic structure, via the choice of a complex polarization. I will explain how this framework may be deformed, making contact with noncommutative algebraic geometry. The main tool will be the deformation of the complex polarization to a generalized complex polarization. This is joint work with Francis Bischoff (arXiv:2108.01658).

algebraic geometrycategory theoryquantum algebrarings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Noncommutative Shapes - halfway event