Growth of groups
Connections for Women: Geometric Group Theory August 17, 2016 - August 19, 2016
Location: MSRI: Simons Auditorium
geometric group theory
finitely generated groups
Day's fixed point theorem
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
20F10 - Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70]
20E15 - Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
Growth functions of groups have been studied intensively in geometric group theory. Regarded up to affine rescaling, they give a group invariant called the growth rate, and there are long-standing questions about possible growth rates for finitely generated groups. Another stream of questions asks whether the growth values satisfy a recursion, a property which is called rational growth and depends on the choice of generators. I will survey the area and discuss the classic proofs that hyperbolic groups and virtually abelian groups have rational growth in any generators
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