Jianya Liu: Manin's conjecture for singular cubic hypersurfaces

Abstract: We establish an asymptotic formula for the number of rational points of bounded height on a class of singular cubic hypersurfaces. This result proves Manin's conjecture for the above hypersurfaces. It is a modest start on the study of rational points on those singular cubic hypersurfaces which are not covered by the classical theorems in this direction. This is a joint work with Jie Wu and Yongqiang Zhao.