Growth in groups: ideas and perspectives

2013/03/01 by Helfgott, H. A. · 1 citation
#05C25 #11B30 #20B05 #20D60 #20F69 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1303.0239

Abstract

This is a survey of methods developed in the last few years to prove results on growth in non-commutative groups. These techniques have their roots in both additive combinatorics and group theory, as well as other fields. We discuss linear algebraic groups, with SL₂(Z/pZ) as the basic example, as well as permutation groups. The emphasis lies on the ideas behind the methods.

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• On the heat kernel of a Cayley graph of PSL₂ℤ

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