  In the geometric version of the Langlands correspondence, irregular singular
point connections play the role of Galois representations with wild
ramification. In this paper, we develop a geometric theory of fundamental
strata to study irregular singular connections on the projective line.
Fundamental strata were originally used to classify cuspidal representations of
the general linear group over a local field. In the geometric setting,
fundamental strata play the role of the leading term of a connection. We
introduce the concept of a regular stratum, which allows us to generalize the
condition that a connection has regular semisimple leading term to connections
with non-integer slope. Finally, we construct a symplectic moduli space of
meromorphic connections on the projective line that contain a regular stratum
at each singular point.
