BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eleni Tzanaki (University of Crete) DTSTART:20221128T140000Z DTEND:20221128T150000Z DTSTAMP:20260423T021330Z UID:GANT/16 DESCRIPTION:Title: Sy mmetric decompositions\, triangulations and real-rootedness\nby Eleni Tzanaki (University of Crete) as part of Greek Algebra & Number Theory Sem inar\n\n\nAbstract\nA triangulation of a simplicial complex $Δ$ is said t o be uniform if the $f$-vector of its restriction to a face of $Δ$ depend s only on the dimension of that face. The notion of uniform triangulation was introduced by Christos Athanasiadis in order to conveniently unify man y well known types of triangulations such as barycentric\, $r$-colored bar ycentric\, $r$-fold edgewise etc. These triangulations have the common fea ture that\, for certain "nice" classes of simplicial complexes $Δ$\, the $h$-polynomial of the triangulation $Δ^′$ of $Δ$\, is real rooted with nonnegative coefficients. Athanasiadis proved that\, uniform triangulatio ns having the so called stong interlacing property\, have real rooted $h$- polynomials with nonnegative coefficients.\n\nWe continue this line of res earch and we study under which conditions the $h$-polynomial of a uniform triangulation $Δ^′$ of $Δ$ has a nonnegative real rooted symmetric dec omposition. We also provide conditions under which this decomposition is a lso interlacing. Applications yield new classes of polynomials in geometri c combinatorics which afford nonnegative\, real-rooted symmetric decomposi tions. Some interesting questions in $h$-vector theory arise from this wor k.\n\nThis is joint work with Christos Athanasiadis.\n LOCATION:https://researchseminars.org/talk/GANT/16/ END:VEVENT END:VCALENDAR