Existence problems for rational points


        Olivier Wittenberg
        (visiting Rice)

  ABSTRACT:

   We shall first describe some of the guiding problems of arithmetic geometry
  which concern the structure of rational points on algebraic varieties, and
  try to give a general picture of their current status.  We then focus on the
  existence problem for rational varieties and its relation with Brauer
  groups.  As time permits, we shall mention recent progress in the case of
  (not necessarily rational) elliptic surfaces, with applications to rational
  varieties.