  Let G be a simple complex algebraic group. We prove that the irregularity of
the adjoint connection of an irregular flat G-bundle on the formal punctured
disk is always greater than or equal to the rank of G. This can be considered
as a geometric analogue of a conjecture of Gross and Reeder. We will also show
that the irregular connections with minimum adjoint irregularity are precisely
the (formal) Frenkel-Gross connections.
