Extending meromorphic connections to coadmissible ̑𝒟-modules

We investigate when a meromorphic connection on a smooth rigid analytic variety 𝑋 gives rise to a coadmissible D ⏜ X \overparen{\mathcal{D}}_{X} -module, and show that this is always the case when the roots of the corresponding 𝑏-functions are all of positive type. We also use this theory to give an example of an integrable connection on the punctured unit disk whose pushforward is not a coadmissible module.

Fundamental two-forms for isomonodromic deformations

We give a simple explicit description of the fundamental two-forms for the isomonodromic deformations of unramified compatibly framed meromorphic connections on the Riemann sphere with arbitrary complex reductive structure group and calculate their Hamiltonians.