Stein fillings and SU(2) representations

Instanton Floer homology is a powerful gauge theoretic invariant of 3-manifolds which
by construction contains useful information about their fundamental groups.  I will outline
its construction, review some facts about Stein manifolds, and then explain a surprising
new connection between the two, proved in joint work with John Baldwin: if a homology
3-sphere bounds a Stein surface which is not a homology 4-ball, then its instanton Floer
homology is nontrivial and hence its fundamental group admits a nontrivial representation
to SU(2).