BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Katie Reilly (UEA) DTSTART:20260203T140000Z DTEND:20260203T150000Z DTSTAMP:20260421T153914Z UID:UEAPS/68 DESCRIPTION:Title: O ne-Relator Inverse Monoids with Decidable Word Problem Are Algorithmically Unclassifiable\nby Katie Reilly (UEA) as part of ANTLR seminar\n\nLec ture held in EFRY 01.10.\n\nAbstract\nA classical result from Combinatoria l Group Theory\, the Adian-Rabin Theorem\, states that there does not exis t an algorithm which takes a finitely presented group G and decides whethe r G possesses a given Markov property. An example of such a property is ha ving decidable word problem. Consequently\, there is no algorithm that tak es a finitely presented group and decides whether the group has decidable word problem. On the other hand\, Magnus proved in the 1930s that every on e-relator group has decidable word problem\, so in the one-relator case su ch an algorithm (trivially) does exist.\n\nIn contrast\, in 2019\, Gray pr oved that there exists a one-relator inverse monoid with undecidable word problem. One key question arising from that work is whether it might be po ssible to classify the one-relator inverse monoids with decidable word pro blem. Related to this one can ask whether there is an algorithm that takes a one-relator inverse monoid as input and decides whether or not that one -relator inverse monoid has decidable word problem.\n\nIn this talk\, I wi ll show that there does not exist an algorithm which takes a one-relator i nverse monoid M as input and decides whether M has decidable word problem. In other words\, the one-relator inverse monoids with decidable word prob lem are algorithmically unclassifiable.\n LOCATION:https://researchseminars.org/talk/UEAPS/68/ END:VEVENT END:VCALENDAR