Abstract
Techniques introduced by Bourgain were applied and extended by Ponce and Vega to the Korteweg-deVries
equation leading to a sharp local-in-time result in the standard Sobolev spaces H^s, s>-3/4. It is conjectured
that  local well- posedness implies global wellposedness for KdV. I plan to survey the wellposedness theory of
KdV,   motivate considering the initial value problem with rough data and describe recent progress towards
the  global-in-time conjecture.