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From Thurston's Corrugations to Smooth Fractals

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Speaker: Vincent Borrelli, Maître de conférences, Université Claude Bernard - Lyon 1
Event date: Tuesday, 25 February 2020 04:30 pm - 05:20 pm
Place: Université du luxembourg
Belval Campus, Maison du Savoir, room 3.110
2, avenue de l'Université, L4365 Esch-sur-Alzette

This conference is part of the MAST Lecture Series organised by the Mathematics Department of the University of Luxembourg with the support of the FNR. The objective is to share the most recent developments of mathematics and their applications in the Luxembourg scientific community.


The Theory of Corrugations is developped in the 70's by Thurston to dispel the mysterious reputation of the Smale's theorem on sphere immersions. A famous corollary of this theorem states that it is possible to smoothly and continuously turn a sphere inside out without creating any crease. The Theory of Corrugations provides both a geometric insight and a general method to construct eversions. By the way, the method is used in the 90's to produce a computer-graphics animation of a sphere eversion. Meanwhile, it is realized that corrugations also appear in the heart of another celebrated result, the C1 Nash embedding Theorem. This theorem considers isometric maps - i. e. maps that preserve the length of curves- with regularity C1 and has numerous paradoxical corollaries. For instance, it is possible to achieve an isometric eversion of the sphere. The study of these C1 isometric maps puts into light unusual objects halfway between fractals and ordinary surfaces: smooth fractals.


Vincent Borrelli, from the University of Lyon, works on the interface of geometry, analysis and computational mathematics. Notable results include his work together with S. Jabrane, F. Lazarus et B. Thibert on explicit embeddings of flat tori in Euclidean space. He is also an active outreacher with many articles in popular science magazines and is actively engaged in widely communicating the beauty of mathematics.

Link: MAST Lecture series