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SUMMARY:Fixed points of group homomorphisms and the Post Correspondence Pr
 oblem - Laura Ciobanu (Heriot-Watt University)
DTSTART:20211203T134500Z
DTEND:20211203T144500Z
UID:TALK162883@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:The Post Correspondence Problem (PCP) is a classical problem i
 n computer science that can be stated as: is it decidable whether given tw
 o morphisms g and h between two free semigroups A and B\, there is any non
 trivial x in A such that g(x)=h(x)? This question can be phrased in terms 
 of equalisers\, asked in the context of free groups\, and expanded: if the
  `equaliser' of g and h is defined to be the subgroup consisting of all x 
 where g(x)=h(x)\, it is natural to wonder not only whether the equaliser i
 s trivial\, but what its rank or basis might be. \n\nWhile the PCP for se
 migroups is famously insoluble and acts as a source of undecidability in m
 any areas of computer science\, the PCP for free groups is open\, as are t
 he related questions about rank\, basis\, or further generalisations. Howe
 ver\, in this talk we will show that there are links and surprising equiva
 lences between these problems in free groups\, and classes of maps for whi
 ch we can give complete answers (joint work with Alan Logan). I will also 
 give an overview of what is known about the PCP in hyperbolic groups and b
 eyond.
LOCATION:In person if possible
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