### Weak weak approximation for del Pezzo surfaces of degree 2

Heilbronn Number Theory Seminar

15th February 2023, 4:00 pm – 5:00 pm

Fry Building, 2.04

Let X be an algebraic variety over a number field k. In arithmetic geometry we are interested in the set X(k) of k-rational points on X. Questions one might ask are, is X(k) empty or not? And if it is not empty, how `large' is X(k)? Del Pezzo surfaces are surfaces classified by their degree d, which is an integer between 1 and 9 (for d at least 3, these are the smooth surfaces of degree d in projective d-space). The lower the degree, the more complex del Pezzo surfaces are. After giving an overview of different notions of `many' rational points and what is known so far for del Pezzo surfaces, I will focus on work in progress joint with Julian Demeio and Sam Streeter on so-called weak weak approximation for del Pezzo surfaces of degree 2.

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