Let X be a complex manifold and let M be a meromorphic connection on X with

poles along a normal crossing divisor D. Levelt-Turrittin theorem asserts that the pull-back of M to the formal neighbourhood of a codimension 1 point in D decom poses (after ramification) into elementary factors easy to work with.

This decomposition may not hold at some other points of D. When it does, we say

that M has good formal decomposition along D. A conjecture of Sabbah, recently

proved by Kedlaya and Mochizuki independently, asserts roughly the

existence of a chain p:Y-->X of blow-ups above D such that p*M has a good formal decomposition along p^{-1}(D).

In a sense, this result is to meromorphic connections what Hironaka desingularization

is to varieties, and has recently allowed ground-breaking progresses

in our understanding of D-modules.

The goal of this talk is to explain in detail the statement of Kedlaya-Mochizuki

theorem and to give some applications.

poles along a normal crossing divisor D. Levelt-Turrittin theorem asserts that the pull-back of M to the formal neighbourhood of a codimension 1 point in D decom poses (after ramification) into elementary factors easy to work with.

This decomposition may not hold at some other points of D. When it does, we say

that M has good formal decomposition along D. A conjecture of Sabbah, recently

proved by Kedlaya and Mochizuki independently, asserts roughly the

existence of a chain p:Y-->X of blow-ups above D such that p*M has a good formal decomposition along p^{-1}(D).

In a sense, this result is to meromorphic connections what Hironaka desingularization

is to varieties, and has recently allowed ground-breaking progresses

in our understanding of D-modules.

The goal of this talk is to explain in detail the statement of Kedlaya-Mochizuki

theorem and to give some applications.

## Date:

Mon, 07/12/2015 - 16:00 to 17:15

## Location:

Ross Building, room 70A