Breaking the duality in the return times theorem
  We prove Bourgain's Return Times Theorem for a range of exponents $p$ and $q$ that are outside the duality range. An oscillation result is used to prove hitherto unknown almost everywhere convergence for the signed average analog of Bourgain's averages. As an immediate corollary we obtain a Wiener-Wintner type of result for the ergodic Hilbert series. 
Ciprian Demeter, Michael Lacey, Terence Tao and Christoph Thiele