BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrew Brooke-Taylor (University of Leeds) DTSTART:20260928T140000Z DTEND:20260928T150000Z DTSTAMP:20261006T044749Z UID:UEAPS/80 DESCRIPTION:Title: M any-generator free self-distributive algebras of embeddings\nby Andrew Brooke-Taylor (University of Leeds) as part of ANTLR seminar\n\nLecture h eld in SCI 0.31.\n\nAbstract\nAn "LD-algebra" or "shelf" is an algebraic s tructure with a binary operation * satisfying the left-self-distributive l aw a*(b*c)=(a*b)*(a*c).  Natural examples include the conjugation operati on on any group\, and weighted means.  In the 1990s\, Laver showed that f rom one of the strongest set theoretic axioms not known to be inconsistent \, "I3"\, one obtains a free singly-generated LD-algebra of embeddings wit h a natural "application" operation.  In particular\, the surrounding set theoretic structure allows one to prove various purely algebraic statemen ts about singly-generated LD-algebras\, some of which to this day are only known under the assumption of I3.  It is thus natural to ask whether suc h free embedding algebras can be obtained with more generators.  I will t alk about recent work with Scott Cramer and Sheila Miller Edwards\, also u sing ideas from Gabe Goldberg\, showing that one can indeed get a two gene rator free LD-algebra from the assumption of I3\, and about further work w ith Sheila Miller Edwards extending this to any number of generators up to continuum.\n LOCATION:https://researchseminars.org/talk/UEAPS/80/ END:VEVENT END:VCALENDAR