A quantization of a Poisson algebra is a noncommutative filtered algebra which recovers the Poisson algebra by the associated graded construction, which we call "taking the semiclassical limit". The quantization problem, which has its roots in the earliest formulation of quantum mechanics, asks us to invert this procedure. To be more precise, given a graded Poisson algebra, can we find/classify quantizations.

In this talk I will consider quantizations of the algebras of regular functions on closures of nilpotent coadjoint orbits for general linear group over fields of positive characteristics p > 0. We classify these quantizations by relating them to certain representations of a finite W-algebra. The result is similar to a theorem of Losev over the complex numbers, however the methods are quite different. This is a joint work with Matt Westaway (Bath) and Filippo Ambrosio (Jena).