BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Martina Juhnke-Kubitzke (University of Osanbrueck) DTSTART:20210408T200000Z DTEND:20210408T213000Z DTSTAMP:20260423T021430Z UID:FOTR/45 DESCRIPTION:Title: Th e antiprism triangulation\nby Martina Juhnke-Kubitzke (University of O sanbrueck) as part of Fellowship of the Ring\n\n\nAbstract\nThe antiprism triangulation provides a natural way to subdivide a simplicial complex $\\ Delta$\, similar to barycentric subdivision\, which appeared independently in combinatorial algebraic topology and computer science. It can be defin ed as the simplicial complex of chains of multi-pointed faces of $\\Delta$ from a combinatorial point of view\, and by successively applying the ant iprism construction\, or balanced stellar subdivisions\, on the faces of $ \\Delta$ from a geometric point of view.\nIn this talk\, we will study enu merative invariants associated to this triangulation\, such as the transfo rmation of the $h$-vector of $\\Delta$ under antiprism triangulation\, the local $h$-vector\, and algebraic properties of its Stanley--Reisner ring. Among other results\, it is shown that the $h$-polynomial of the antipris m triangulation of a simplex is real-rooted and that the antiprism triangu lation of $\\Delta$ has the almost strong Lefschetz property over $\\mathb b{R}$ for every shellable complex $\\Delta$.\n\nI will make the talk as se lf-contained as possible\, and assume no previous knowledge of combinatori cs of subdivisions. This is joint work with Christos Athanasiadis and Jan- Marten Brunink.\n LOCATION:https://researchseminars.org/talk/FOTR/45/ END:VEVENT END:VCALENDAR