Noncommutative local monodromy theorem

Let $X\to D^*$ be a family of smooth projective varieties over the punctured disk.
The Griffiths-Landman-Grothendieck “Local Monodromy Theorem” asserts that the Gauss-Manin connection on the de Rham cohomology $H^*_{DR}(X/D^*)$ has a regular singularity at the origin and that the monodromy of this connection is quasi-unipotent. I will discuss a noncommutative generalization of this result, where the de Rham cohomology is replaced by the periodic cyclic homology of a smooth proper $DG$ algebra over $D^*$ equipped with the Gauss-Manin-Getzler connection.
This talk is based on a joint work with Dmitry Vaintrob.