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SUMMARY:Laura Ciobanu (Herriot Watt)
DTSTART:20210419T080000Z
DTEND:20210419T090000Z
DTSTAMP:20260423T021353Z
UID:SiN/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/17/">Fre
 e group homomorphisms and the Post Correspondence Problem</a>\nby Laura Ci
 obanu (Herriot Watt) as part of Symmetry in Newcastle\n\n\nAbstract\nThe P
 ost Correspondence Problem (PCP) is a classical problem in computer scienc
 e that can be stated as: is it decidable whether given two morphisms $g$ a
 nd $h$ between two free semigroups $A$ and $B$\, there is any nontrivial $
 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 `e
 qualiser' 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 equali
 ser is trivial\, but what its rank or basis might be.\n\nWhile the PCP for
  semigroups is famously insoluble and acts as a source of undecidability i
 n many areas of computer science\, the PCP for free groups is open\, as ar
 e the related questions about rank\, basis\, or further generalisations. H
 owever\, in this talk we will show that there are links and surprising equ
 ivalences between these problems in free groups\, and classes of maps for 
 which we can give complete answers. This is joint work with Alan Logan.\n
LOCATION:https://researchseminars.org/talk/SiN/17/
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