Short Egyptian fractions

Abstract: Given a fraction $a/b \in (0, 1)$, write it as a sum of distinct unit fractions. What is the least number of unit fractions you need? Over $75$ years ago, Erd\H{o}s conjectured that $O(\log \log b)$ unit fractions always suffices, which would be optimal if true. This conjecture was recently proven by an internal model of OpenAI, and in this talk we aim to explain a simplified version of the proof, which was obtained in joint work with Thomas Bloom.

commutative algebracombinatoricsnumber theory

Audience: researchers in the topic

New York Number Theory Seminar

Series comments: Meeting ID: 840 6618 4717 Passcode: 304403