From the index of a differential operator to the Milnor number of singularity

In this paper I begin by recalling the outline of my Master's thesis, written under the direction of Jairo Charris, and go on to survey some related ideas due to Malgrange. I end by explaining how Malgrange used the Gauss-Manin connection to calculate the Milnor number (the rank of the vanishing homology) of an isolated hypersurface singularity