BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matthew Baker (Georgia Tech School of Mathematics) DTSTART:20221004T200000Z DTEND:20221004T210000Z DTSTAMP:20260423T040228Z UID:Matroids/1 DESCRIPTION:Title: Foundations of Matroids\nby Matthew Baker (Georgia Tech School of Mat hematics) as part of Matroids - Combinatorics\, Algebra and Geometry Semin ar\n\nLecture held in Room 210\, The Fields Institute.\n\nAbstract\nMatroi d theorists are interested in questions concerning representability of mat roids over fields. More generally\, one can ask about representability ove r partial fields in the sense of Semple and Whittle. Pendavingh and van Zw am introduced the universal partial field of a matroid\, which governs the representations of over all partial fields. Unfortunately\, most matroids are not representable over any partial field\, and in this case\, the uni versal partial field is not defined. Oliver Lorscheid and I have introduce d a generalization of the universal partial field which we call the founda tion of a matroid\; it is always well-defined. The foundation is a type of algebraic object which we call a pasture\; pastures include both hyperfie lds and partial fields. As a particular application of this point of view\ , I will explain the classification of all possible foundations for matroi ds having no minor isomorphic to U(2\,5) or U(3\,5). Among other things\, this provides a short and conceptual proof of the 1997 theorem of Lee and Scobee which says that a matroid is both ternary and orientable if and onl y if it is dyadic.\n LOCATION:https://researchseminars.org/talk/Matroids/1/ END:VEVENT END:VCALENDAR