# Vinay Kumaraswamy: Counting rational points on cubic hypersurfaces

**Time: **
Thu 2023-10-26 13.15 - 14.15

**Location: **
KTH, 3418

**Participating: **
Vinay Kumaraswamy (KTH)

**Abstract.**

Let *X* be a cubic hypersurface cut out by a non-degenerate rational cubic form in *n* variables. If *n* is at least 14, then Heath-Brown has shown that *X* has at least one non-trivial rational point. By a result of Kollár, this implies that there are infinitely many rational points on *X*. In this talk, I will discuss the problem of obtaining quantitative lower bounds for the number of rational points of bounded height on *X*.