  We study dynamics of the horocycle flow on strata of translation surfaces,
introduce new invariants for ergodic measures, and analyze the interaction of
the horocycle flow and real Rel surgeries. We use this analysis to complete and
extend results of Calta and Wortman classifying horocycle-invariant measures in
the eigenform loci. We classify the orbit-closures and prove that every orbit
is equidistributed in its orbit-closure. We also prove equidistribution
statements regarding limits of sequences of measures, some of which have
applications to counting problems.
