Description
By the Riemann-Hilbert correspondence, complex linear ODEs with polynomial coefficients, or more geometrically connections with regular singularities on curves, are characterized by their monodromy data. This admits a generalization to the case of irregular singularities, involving generalized monodromy data known as Stokes data. On the other hand, there is a notion of the Fourier transform for irregular connections on the Riemann sphere: it acts in a nontrivial way, typically changing the rank, number of singularities, and pole orders of the connections. In this talk, I will present a topological way to compute the Stokes data of the Fourier transform of a connection in terms of its Stokes data in a new class of cases, relying on work of T. Mochizuki. In particular, this gives explicit isomorphisms between the corresponding wild character varieties. This is joint work with Andreas Hohl.