BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kathlén Kohn (KTH\, Stockholm) DTSTART:20200619T123000Z DTEND:20200619T133000Z DTSTAMP:20260423T041158Z UID:GandT/7 DESCRIPTION:Title: Pr ojective geometry of Wachspress coordinates.\nby Kathlén Kohn (KTH\, Stockholm) as part of The London geometry and topology seminar\n\n\nAbstra ct\nThis talk brings many areas together: discrete geometry\, statistics\, intersection theory\, classical algebraic geometry\, and geometric modeli ng.\nFirst\, we recall the definition of the adjoint of a polytope given b y Warren in 1996 in the context of geometric modeling. He defined this pol ynomial to generalize barycentric coordinates from simplices to arbitrary polytopes. Secondly\, we show how this polynomial appears in statistics. I t is the numerator of a generating function over all moments of the unifor m probability distribution on a polytope. Thirdly\, we characterize the ad joint via a vanishing property: it is the unique polynomial of minimal deg ree which vanishes on the non-faces of a polytope. In addition\, we see th at the adjoint appears as the central piece in Segre classes of monomial s chemes. Finally\, we observe that adjoints of polytopes are special cases of the classical notion of adjoints of divisors. Since the adjoint of a si mple polytope is unique\, the corresponding divisors have unique canonical curves. In the case of three-dimensional polytopes\, we show that these d ivisors are either K3- or elliptic surfaces.\nThis talk is based on joint works with Kristian Ranestad\, Boris Shapiro and Bernd Sturmfels\n LOCATION:https://researchseminars.org/talk/GandT/7/ END:VEVENT END:VCALENDAR