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DTSTART;TZID=America/New_York:20210113T090000
DTEND;TZID=America/New_York:20210113T100000
DTSTAMP:20240529T173823Z
CREATED:20240215T093336Z
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UID:10002720-1610528400-1610532000@cmsa.fas.harvard.edu
SUMMARY:A universal triangulation for flat tori
DESCRIPTION:Speaker:Francis Lazarus\, CNRS / Grenoble University \nTitle: A universal triangulation for flat tori \nAbstract: A celebrated theorem of Nash completed by Kuiper implies that every smooth Riemannian surface has a C¹ isometric embedding in the Euclidean 3-space E³. An analogous result\, due to Burago and Zalgaller\, states that every polyhedral surface\, obtained by gluing Euclidean triangles\, has an isometric PL embedding in E³. In particular\, this provides PL isometric embeddings for every flat torus (a quotient of E² by a rank 2 lattice). However\, the proof of Burago and Zalgaller is partially constructive\, relying on the Nash-Kuiper theorem. In practice\, it produces PL embeddings with a huge number of vertices\, moreover distinct for every flat torus. Based on a construction of Zalgaller and on recent works by Arnoux et al. we exhibit a universal triangulation with less than 10.000 vertices\, admitting for any flat torus an isometric embedding that is linear on each triangle. Based on joint work with Florent Tallerie.
URL:https://cmsa.fas.harvard.edu/event/1-13-2022-interdisciplinary-science-seminar/
LOCATION:Virtual
CATEGORIES:Interdisciplinary Science Seminar
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