Affiliation:
Northwestern
Date:
Mon, 19/06/2017 - 11:00 - 12:00
Given a symplectic manifold $M$, one can consider its deformation quantization, i.e. an associative multiplication law on functions on $M$ that depends on a formal parameter $h$. When $M$ is the cotangent bundle of a manifold $X$, one essentially recovers the algebra of differential operators on $X$, or rather of $h$-differential operators $P(x, hd/dx)$. Modules over differential operators are well known to have interesting applications to PDE and other topics, so it is natural to hope that modules over deformation quantization would be interesting as well.