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SUMMARY:Eduardo Martinez-Pedroza (Memorial University of Newfoundland)
DTSTART:20201217T130000Z
DTEND:20201217T140000Z
DTSTAMP:20260423T024648Z
UID:AlBicocca/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AlBicocca/8/
 ">Quasi-isometric rigidity of subgroups</a>\nby Eduardo Martinez-Pedroza (
 Memorial University of Newfoundland) as part of Al@Bicocca take-away\n\n\n
 Abstract\nA central theme in geometric group theory: what are the relation
 s between the algebraic and geometric properties of a finitely generated g
 roup. Finitely generated groups with "equivalent" geometries are called qu
 asi-isometric. Let $G$ and $H$ be quasi-isometric finitely generated group
 s and let $P$ be a subgroup of $G$. Is there a subgroup $Q$ (or a collecti
 on of subgroups) of $H$ whose left cosets coarsely reflect the geometry of
  the left cosets of $P$ in $G$? We explore sufficient conditions on the pa
 ir $(G\,P)$ for a positive answer. In the talk\, we introduce notions of q
 uasi-isometric pairs\, and quasi-isometrically characteristic collection o
 f subgroups. Distinct classes of qi-characteristic collections of subgroup
 s have been studied in the literature on quasi-isometric rigidity\, we wil
 l describe some of them. The talk will focus on putting context to our mai
 n result and illustrate it with some applications: If $G$ and $H$ are fini
 tely generated quasi-isometric groups and $P$ is a qi-characteristic colle
 ction of subgroups of $G$\, then there is a collection of subgroups $Q$ of
  $H$ such that $(G\, P)$ and $(H\, Q)$ are quasi-isometric pairs.\nThis is
  joint work with Jorge Luis Sanchez (UNAM\, Mexico).\n
LOCATION:https://researchseminars.org/talk/AlBicocca/8/
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