# Geometry and Mathematical Physics Seminar 2011/2012

Thursday 16 February 2012. The Frank Adams Room (Room 1.212), the Alan Turing Building. 3pm

## Quantization and Full Symbol Calculus on Lie Algebroids 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.