Algebraic flat connections and o-minimality

We prove that an algebraic flat connection has $ {\mathbb R}_{\rm{ an, \  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 Gauss-Manin connection.

Joint work with Moritz Kerz.