# Rational lines on cubic hypersurfaces

## Julia Brandes

One of the most intensely studied question in the intersection of analytic
number theory and algebraic geometry concerns the existence and
distribution of rational points on cubic hypersurfaces, but the analogous
question regarding lines or higher-dimensional linear spaces is far less
understood. In this talk, we will show that every smooth cubic hypersurface
of projective dimension at least 29 contains a rational line, superseding
earlier bounds due to Dietmann and Wooley. This is joint work with Rainer
Dietmann.