Growth of groups
Connections for Women: Geometric Group Theory August 17, 2016 - August 19, 2016
Location: SLMath: Eisenbud Auditorium
geometric group theory
word problem
Dehn function
length function
Cannon's theorem
CAT(0) group
finitely generated groups
hyperbolic group
20Jxx - Connections of group theory with homological algebra and category theory
00A35 - Methodology of mathematics {For mathematics education, see 97-XX}
20-01 - Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory
20-04 - Software, source code, etc. for problems pertaining to group theory
14583
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
Duchin Notes
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