On the exceptional set in the $abc$ conjecture

Abstract: The well-known $abc$ conjecture asserts that for any coprime triple of positive integers satisfying $a+b=c$ the squarefree radical of $abc$ satisfies a certain strong inequality. 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.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html