BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matt Baker (Georgia Tech) DTSTART:20211209T150000Z DTEND:20211209T160000Z DTSTAMP:20260422T070025Z UID:CJCS/45 DESCRIPTION:Title: Th e Foundation of a Matroid\nby Matt Baker (Georgia Tech) as part of Cop enhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nMatroid theorists a re interested in questions concerning representability of matroids over fi elds. More generally\, one can ask about representability over partial fie lds in the sense of Semple and Whittle. Pendavingh and van Zwam introduced the universal partial field of a matroid\, which governs the representati ons of over all partial fields. Unfortunately\, most matroids are not rep resentable over any partial field\, and in this case\, the universal parti al field is not defined.\n\nOliver Lorscheid and I have introduced a gener alization of the universal partial field which we call the foundation of a matroid\; it is always well-defined. The foundation is a type of algebrai c object which we call a pasture\; pastures include both hyperfields and p artial fields. As a particular application of this point of view\, I will explain the classification of all possible foundations for matroids having no minor isomorphic to U(2\,5) or U(3\,5). Among other things\, this prov ides a short and conceptual proof of the 1997 theorem of Lee and Scobee wh ich says that a matroid is both ternary and orientable if and only if it i s dyadic.\n LOCATION:https://researchseminars.org/talk/CJCS/45/ END:VEVENT END:VCALENDAR