Adam Biggs (University of Manchester)
Adam.Biggs@student.manchester.ac.uk
We shall outline a method of quantization which in principle considers replacing graded algebras by suitable filtered algebra via full symbol calculus - this process has its motivation in deformation quantization where we consider a new multiplication up to $O(h)$. In particular we shall calculate the equivalence classes when we have a Lie algebroid $E$, and focus on the case of $TM$, with the trivial structure, and $T^*M$ with the structure induced from a Poisson manifold $M$.
Time permitting we shall then explain how this can be extended to the algebra of densities on a manifold for the cotangent bundle, and outline methods to introduce formal parameters into the setup.