# The diameter of the symmetric group: ideas and tools

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.