BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Kompatscher (Charles University Prague) DTSTART:20211130T190000Z DTEND:20211130T200000Z DTSTAMP:20260423T004754Z UID:PALS/22 DESCRIPTION:Title: G- terms and the local-global property\nby Michael Kompatscher (Charles U niversity Prague) as part of PALS Panglobal Algebra and Logic Seminar\n\n\ nAbstract\nLet $G$ be a permutation group on a $n$-element set. We then sa y that an algebra $\\mathbf A$ has a $G$-term $t(x_1\,\\ldots\,x_n)$\, if $t$ is invariant under permuting its variables according to $G$\, i.e. $\\ mathbf A \\models t(x_1\,\\ldots\,x_n) \\approx t(x_{\\pi(1)}\,\\ldots\,x_ {\\pi(n)})$ for all $\\pi \\in G$. Since $G$-terms appear in the study of constraint satisfaction problems and elsewhere\, it is natural to ask for their classification up to interpretability. In the first part of my talk I would like to share a few partial results on this problem.\n\nIn the sec ond part I am going to discuss the complexity of deciding whether a given finite algebra has a $G$-term. The most commonly used strategy in showing that deciding a given Maltsev condition is in P\, is to show that it suffi ces to check the condition locally (i.e. on subsets of bounded size). We s how that this „local-global“ approach works for all $G$-terms induced by regular permutation groups $G$ (and direct products of them)\, but fail s for some other „rich enough" permutation groups\, such as $Sym(n)$ for $n \\geq 3$.\n\nThis is joint work with Alexandr Kazda.\n LOCATION:https://researchseminars.org/talk/PALS/22/ END:VEVENT END:VCALENDAR