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The diameter of the symmetric group: ideas and tools

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NPCW04 - Approximation, deformation, quasification

Given a finite group \ and a set \ of generators, the diameter \\\\ \\\\\\\\ of the Cayley graph \\\\\\ is the smallest \ such that every element of \ can be expressed as a word of length at most \ in \\ \ "> . We are concerned with bounding \\\\ \\\ \\ \\\ \ \\\\\ \\\\\\\\ .

It has long been conjectured that the diameter of the symmetric group of degree \ is polynomially bounded in \ . In 2011, Helfgott and Seress gave a quasipolynomial bound (exp((log n)
(4+epsilon))). We will discuss a recent, much simplified version of the proof. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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