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SUMMARY:Free-by-cyclic groups: equational Noetherianity and growth rates -
  Motiejus Valiunas (University of Wroclaw)
DTSTART:20250716T104500Z
DTEND:20250716T114500Z
UID:TALK233569@talks.cam.ac.uk
DESCRIPTION:A group G is said to be equationally Noetherian if every syste
 m of equations over G has the same solution set as some finite subsystem.&
 nbsp\; This property\, introduced in the 1990s in the context of algebraic
  geometry over groups\, has found its way into logic over groups and geome
 tric group theory\, in particular the study of limit groups and acylindric
 ally hyperbolic groups.&nbsp\; In this talk\, I will explain why all exten
 sions G of a finitely generated free group by the infinite cyclic group ar
 e equationally Noetherian.&nbsp\; As a consequence\, the set of exponentia
 l growth rates for any such G is well-ordered.&nbsp\; The proofs are based
  on various group actions on trees.\nThis is joint work with Monika Kudlin
 ska.
LOCATION:Seminar Room 1\, Newton Institute
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