BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Elliot Kaplan (McMaster University) DTSTART:20230330T180000Z DTEND:20230330T190000Z DTSTAMP:20260423T035919Z UID:OLS/124 DESCRIPTION:Title: Hi lbert polynomials for finitary matroids\nby Elliot Kaplan (McMaster Un iversity) as part of Online logic seminar\n\n\nAbstract\nEventual polynomi al growth is a common theme in combinatorics and commutative algebra. The quintessential example of this phenomenon is the Hilbert polynomial\, whic h eventually coincides with the linear dimension of the graded pieces of a finitely generated module over a polynomial ring. A later result of Kolch in shows that the transcendence degree of certain field extensions of a di fferential field is eventually polynomial. More recently\, Khovanskii show ed that for finite subsets A and B of a commutative semigroup\, the size o f the sumset A+tB is eventually polynomial in t. I will present a common g eneralization of these three results in terms of finitary matroids (also c alled pregeometries). I’ll discuss other instances of eventual polynomia l growth (like the Betti numbers of a simplicial complex) as well as some applications to bounding model-theoretic ranks. This is joint work with An tongiulio Fornasiero.\n LOCATION:https://researchseminars.org/talk/OLS/124/ END:VEVENT END:VCALENDAR