Alladi Ramakrishnan Hall

Inhomogeneous cubic congruences and rational points on Del Pezzo surfaces

Stephan Baier

TIFR

In 1990, Yuri Manin formulated a far-reaching conjecture that
relates the quantitative behaviour of rational points on Fano varieties
with the geometry of these varieties. Since then, the resolution of this
conjecture, especially for Del Pezzo surfaces (two-dimensional Fano
varieties), has become a very active field of research. As a rule of
thumb, the problem becomes the harder the smaller the degree of the Del
Pezzo surface is. In this talk, I present the key steps of a proof of
Manin's conjecture for a particular Del Pezzo surface of degree 2 by Tim
Browning and myself.