Designed and built with care, filled with creative elements

Top

Counting rational points on conic bundle surfaces

Salle W

In this talk we consider the problem of counting the number of rational points of bounded height on certain intersections of two quadrics in five variables.These are del Pezzo surfaces of degree four, and we focus on the case where the surface has a conic bundle structure.

Squareful points on hyperplanes

Salle W

In this talk, I will explain how one can determine the asymptotic behaviour of the number of integral points on the hyperplane X_0+ ... +X_n=0 for which each coordinate is a squareful number using the classical circle method, given that n>= 4. I will also indicate how this result improves our intuition when considering the problem with only three squareful numbers.

Mordell-Weil Generators for Cubic Surfaces

Salle W

Let C be a smooth plane cubic curve over the rationals. TheMordell--Weil Theorem can be restated as follows: there is a finitesubset B of rational points such that all rational points can beobtained from this subset by successive tangent and secantconstructions. It is conjectured that a minimal such B can bearbitrarily large