BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Duc-Manh Nguyen (Université de Bordeaux) DTSTART:20201117T140000Z DTEND:20201117T150000Z DTSTAMP:20260423T052448Z UID:Geometry/15 DESCRIPTION:Title: Variation of Hodge structure and enumerating triangulations and quadrang ulations of surfaces\nby Duc-Manh Nguyen (Université de Bordeaux) as part of Pangolin seminar\n\n\nAbstract\nSince the work of Eskin-Okounkov ( in 2001)\, it has been known that in any stratum of translation surfaces t he number of square-tiled surafces constructed from at most n squares gro ws like $c\\pi^{2g}n^d$\, where $d$ is the (complex) dimension of the stra tum\, $g$ is the genus of the surfaces\, and $c$ is a rational number. Sim ilar phenomenon also occurs in strata of quadratic differentials. Counting square-tiled surfaces in a given stratum is more or less the same as coun ting quadrangulations of a topological surface\, with some prescribed cond itions on the singularities and the holonomy of the associated flat metric . More recently\, Engel showed that the asymptotics of the numbers of quad rangulations and triangulations\, satisfying some prescribed conditions at the singularities\, with at most $n$ tiles are of the form $\\alpha n^d$\ , where $\\alpha$ is a constant in $Q[\\pi]$ or $Q[\\sqrt{3}\\pi]$.\nIn th is talk\, we will explain how the asymptotics above can be related to the computation of the volume of some moduli spaces\, and how one can show tha t in some situations the constant $\\alpha$ belongs actually to either $Q\ \cdot\\pi^d$\, or $Q\\cdot(\\sqrt{3}\\pi)^d$ by using tools from complex a lgebraic geometry. This is joint work with Vincent Koziarz.\n LOCATION:https://researchseminars.org/talk/Geometry/15/ END:VEVENT END:VCALENDAR