**Jyoti Singh**

MNNIT, Allahabad

October 16, 2014

**An algebraic proof of the Involutivity theorem**:
An important geometric invariant in the theory of $D$-modules is the
characteristic variety and its involutivity is a vital result in this
theory. In this talk, we discuss an algebraic proof of the involutivity
theorem which says that the characteristic ideal of a module is closed
under a Poisson bracket.