Algebraic Flat Connections and O-Minimality

We prove that an algebraic flat connection has ℝan, exp

-definable flat sections if and only if it is regular singular with unitary monodromy eigenvalues at infinity, refining previous work of Bakker–Mullane. This provides e.g. an o-minimal characterization of classical properties of the *Gau{\ss}-Manin connection*. Joint with Moritz Kerz

*[I lectured on this in summer, two or three of the speakers were in attendance. In the mean time, there  has been modest progress, albeit some  little setback as well.]