On irregularities of Fourier transforms of regular holonomic D-modules

Fourier transforms of regular holonomic D-modules are not regular in general. In this talk, we introduce our recent results on their irregularities. First, by using the irregular Riemann-Hilbert correspondence of D'Agnolo-Kashiwara and the theory of Fourier-Sato transforms for enhanced ind-sheaves of Kashiwara-Schapira etc., we obtain a formula for their enhanced solution complexes. Then we show that the irregularities of the Fourier transforms are expressed by the geometries of the original D-modules. The result can be applied to A-hypergeometric functions.
This is a joint work with Yohei Ito.