Ritabrata Munshi (Rutgers)
Title: Counting rational points on cubics and quartics.
Abstract: While the problem of counting the number of rational points on
del Pezzo surfaces of high degrees has been successfully tackled using
geometric techniques, that of lower degrees still remains out of reach of
the present methods.
In this talk, I will describe a joint work with Henryk Iwaniec, where we
use a combination of sieve methods and techniques from analytic number
theory to get bounds for the number of rational points on del Pezzo
surfaces of degree 3 (i.e. cubic surfaces in P3), and of degree
4 (i.e. intersections of two quadrics in P4).