  We calculate the transverse momentum and invariant mass dependence of
elliptic flow of thermal dileptons for Au+Au collisions at the Relativistic
Heavy Ion Collider. The system is described using hydrodynamics, with the
assumption of formation of a thermalized quark-gluon plasma at some early time,
followed by cooling through expansion, hadronization and decoupling. Dileptons
are emitted throughout the expansion history: by annihilation of quarks and
anti-quarks inthe early quark-gluon plasma stage and through a set of hadronic
reactions during the late hadronic stage. The resulting differential elliptic
flow exhibits a rich structure, with different dilepton mass windows providing
access to different stages of the expansion history. Elliptic flow measurements
for dileptons,combined with those of hadrons and direct photons, are a powerful
tool for mapping the time-evolution of heavy-ion collisions.
