BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Brooke Ullery (Emory University) DTSTART:20200813T203000Z DTEND:20200813T220000Z DTSTAMP:20260423T021450Z UID:FOTR/20 DESCRIPTION:Title: Ca yley-Bacharach theorems and measures of irrationality\nby Brooke Uller y (Emory University) as part of Fellowship of the Ring\n\n\nAbstract\nIf Z is a set of points in projective space\, we can ask which polynomials of degree d vanish at every point in Z. If P is one point of Z\, the vanishin g of a polynomial at P imposes one linear condition on the coefficients. T hus\, the vanishing of a polynomial on all of Z imposes |Z| linear conditi ons on the coefficients. A classical question in algebraic geometry\, dati ng back to at least the 4th century\, is how many of those linear conditio ns are independent? For instance\, if we look at the space of lines throug h three collinear points in the plane\, the unique line through two of the points is exactly the one through all three\; i.e. the conditions imposed by any two of the points imply those of the third. In this talk\, I will survey several classical results including the original Cayley-Bacharach T heorem and Castelnuovo’s Lemma about points on rational curves. I’ll t hen describe some recent results and conjectures about points satisfying t he so-called Cayley-Bacharach condition and show how they connect to sever al seemingly unrelated questions in contemporary algebraic geometry relati ng to the gonality of curves and measures of irrationality of higher dimen sional varieties.\n LOCATION:https://researchseminars.org/talk/FOTR/20/ END:VEVENT END:VCALENDAR