Pankaj Vishe: A version of the circle method over number fields.

We present a version of the Hardy-Littlewood circle method for number fields K/Q. We provide an alternative route to the Kloosterman refinement over an arbitrary number field, circumventing the need for Farey dissection  and use it to show that every non-singular projective cubic hypersurface over K always has a K-rational point when it has dimension at least 8. This is a joint work with TIm Browning.