Parabolic hedge eigensheaves introduction

We study the Geometric Langlands Conjecture (GLC) for rank two flat bundles on the projective line C with tame ramification at five points {p(1), p(2), p(3), p(4), p(5)}. In particular we construct the automorphic D-modules predicted by GLC on the moduli space of rank two parabolic bundles on (C, {p(1), p(2), p(3), p(4), p(5)}). The construction uses non-abelian Hodge theory and a Fourier-Mukai transform along the fibers of the Hitchin fibration to reduce the problem to one in classical projective geometry on the intersection of two quadrics in P-4.