BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ashot Minasyan (Southampton) DTSTART:20241015T130000Z DTEND:20241015T140000Z DTSTAMP:20260421T153844Z UID:UEAPS/36 DESCRIPTION:Title: G enerating RAAGs in 1-relator groups\nby Ashot Minasyan (Southampton) a s part of ANTLR seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\nGiven a finite simplicial graph $\\Gamma$\, the right angled Artin group (RAAG) $A(\\Gamma)$ is generated by the vertices of $\\Gamma$ subject to the rela tions that two vertices commute if and only if they are adjacent in $\\Gam ma$. The monoid with the same presentation is called the trace monoid $T(\ \Gamma)$. RAAGs play a significant role in Geometric Group Theory\, while Trace monoids have important applications in Computer Science.\n\nThe trac e monoid $T(\\Gamma)$ is naturally embedded in the RAAG $A(\\Gamma)$\, as the set of positive words. In my talk I will discuss the following problem : suppose that a 1-relator group G contains a submonoid isomorphic to $T(\ \Gamma)$. Does $G$ also contain a copy of $A(\\Gamma)$ as a subgroup?\n\nT his problem is motivated by recent work of Foniqi\, Gray and Nyberg-Brodda \, who proved that groups containing T(P_4)\, where P_4 is the path with 4 vertices (of length 3)\, have undecidable rational subset problem. They a lso exhibited 1-relator groups containing A(P_4) and asked whether every 1 -relator group which has a submonoid isomorphic to T(P_4) must also have a subgroup isomorphic to A(P_4). I will sketch an argument\, based on joint work with Motiejus Valiunas\, showing that the answer to the latter quest ion is positive.\n LOCATION:https://researchseminars.org/talk/UEAPS/36/ END:VEVENT END:VCALENDAR