Seminar series
Date
Thu, 13 Feb 2025
16:00
16:00
Location
Lecture Room 4
Speaker
Joni Teräväinen
Organisation
University of Cambridge
The well known abc conjecture asserts that for any coprime triple of positive integers satisfying $a+b=c$, we have $c<K_{\varepsilon} \mathrm{rad}(abc)^{1+\varepsilon}$, where $\mathrm{rad}$ is the squarefree radical function.
In this talk, I will discuss a proof giving the first power-saving improvement over the trivial bound for the number of exceptions to this conjecture. The proof is based on a combination of various methods for counting rational points on curves, and a combinatorial analysis to patch these cases together.
This is joint work with Tim Browning and Jared Lichtman.