BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Miguel Couceiro (Universite de Lorraine\, France) DTSTART:20211109T200000Z DTEND:20211109T210000Z DTSTAMP:20260423T004727Z UID:PALS/17 DESCRIPTION:Title: Im possibility theorems over median algebras and beyond\nby Miguel Coucei ro (Universite de Lorraine\, France) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nIn this presentation we consider aggregation procedures (consensus functions) over median algebras (ternary algebras t hat subsume several ordered structures such as distributive lattices as we ll as several combinatorial structures such as median graphs). Our startin g point is a recent Arrow type impossibility result that states that any m edian preserving consensus function over linearly ordered sets is trivial in the sense that it only depends on a single argument. In view of this re sult\, a natural problem is then to identify those median algebras that le ad to such impossibility results. In particular\, we will show that such i mpossibility results are inevitable when the codomain contains no cycle\, i.e.\, it is a "tree"\, and we will provide a surprisingly simple conditio n that completely describes the latter as median algebras. To broaden the talk\, we will also present some recent results that answer the parametriz ed version of this problem in which dependence is restricted to k argument s. We will conclude by observing that the underlying property to proving s uch results is that of congruence distributivity\, which naturally raises the question whether these results extend to other varieties of algebras\, e.g.\, congruence modular varieties.\n LOCATION:https://researchseminars.org/talk/PALS/17/ END:VEVENT END:VCALENDAR