Department Research Seminar - Dr. Carlo Pagano

Solvability of conics over the integers

In this talk I will put in context a recent joint work with Peter Koymans, settling a conjecture of Peter Stevenhagen predicting an asymptotic formula for how often the so-called negative Pell equation is solvable over the integers . The talk is aimed for the general mathematical audience. Hence, after stating the main result, in the first half of the talk I will introduce the audience to the obstructions to solve conics (2-variable quadratic equations) over the integers and the rational numbers. In the second half I will give an overview of the proof and its possible applications to other problems.