{"id":8145,"date":"2020-01-20T14:56:20","date_gmt":"2020-01-20T13:56:20","guid":{"rendered":"https:\/\/www.uni.lu\/fr\/events\/from-thurstons-corrugations-to-smooth-fractals\/"},"modified":"2020-01-20T14:56:20","modified_gmt":"2020-01-20T13:56:20","slug":"from-thurstons-corrugations-to-smooth-fractals","status":"publish","type":"events","link":"https:\/\/www.uni.lu\/fr\/events\/from-thurstons-corrugations-to-smooth-fractals\/","title":{"rendered":"From Thurston&rsquo;s Corrugations to Smooth Fractals"},"content":{"rendered":"<section class=\"wp-block-unilux-blocks-free-section section\"><div class=\"container xl:max-w-screen-xl\"><p>This conference is part of the\u00a0<strong>MAST\u00a0Lecture Series\u00a0<\/strong>organised by the Mathematics Department of the University of Luxembourg with the support of the FNR.\u00a0The objective is to share the most recent developments of mathematics and their applications in the Luxembourg scientific community.<\/p><p><strong>Abstract<\/strong><\/p><p>The Theory of Corrugations is developped in the 70&rsquo;s by Thurston to dispel the mysterious reputation of the Smale&rsquo;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&rsquo;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\u00a0Nash embedding Theorem. This theorem considers isometric maps &#8211; i. e. maps that preserve the length of curves- with regularity C1\u00a0and has numerous paradoxical corollaries. For instance, it is possible to achieve an isometric eversion of the sphere. The study of these C1\u00a0isometric maps puts into light unusual objects halfway between fractals and ordinary surfaces: smooth fractals.<\/p><p><strong>Speaker<\/strong><\/p><p>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.<\/p><\/div><\/section>","protected":false},"excerpt":{"rendered":"<p>This conference is part of the\u00a0MAST\u00a0Lecture Series\u00a0organised by the Mathematics Department of the University of Luxembourg with the support of the FNR.\u00a0The objective is to share the most recent developments of mathematics and their applications in the Luxembourg scientific community.<\/p>\n","protected":false},"author":0,"featured_media":8146,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","format":"standard","meta":{"featured_image_focal_point":[],"show_featured_caption":false,"ulux_newsletter_groups":"","uluxPostTitle":"","uluxPrePostTitle":"","_trash_the_other_posts":false,"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"event_start_date":"2020-02-25 16:30:00","event_end_date":"2020-02-25 17:20:00","event_speaker_name":"Vincent Borrelli, Ma\u00eetre de conf\u00e9rences, Universit\u00e9 Claude Bernard - Lyon 1","event_speaker_link":"","event_is_online":false,"event_location":"Universit\u00e9 du luxembourg\r\nBelval Campus, Maison du Savoir, room 3.110\r\n2, avenue de l'Universit\u00e9, L4365 Esch-sur-Alzette","event_street":"","event_location_link":"","event_zip_code":"","event_city":"","event_country":"LU"},"events-topic":[315],"events-type":[],"organisation":[61,25,226],"authorship":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.3 (Yoast SEO v22.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>From Thurston&#039;s Corrugations to Smooth Fractals - Universit\u00e9 du Luxembourg<\/title>\n<meta name=\"description\" content=\"This conference is part of the\u00a0MAST\u00a0Lecture Series\u00a0organised by the Mathematics Department of the University of Luxembourg with the support of the FNR.\u00a0The objective is to share the most recent developments of mathematics and their applications in the Luxembourg scientific community.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.uni.lu\/fr\/events\/from-thurstons-corrugations-to-smooth-fractals\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"From Thurston&#039;s Corrugations to Smooth Fractals\" \/>\n<meta property=\"og:description\" content=\"This conference is part of the\u00a0MAST\u00a0Lecture Series\u00a0organised by the Mathematics Department of the University of Luxembourg with the support of the FNR.\u00a0The objective is to share the most recent developments of mathematics and their applications in the Luxembourg scientific community.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.uni.lu\/fr\/events\/from-thurstons-corrugations-to-smooth-fractals\/\" \/>\n<meta property=\"og:site_name\" content=\"UNI FR\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/uni.lu\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.uni.lu\/wp-content\/uploads\/sites\/11\/2026\/03\/03120045\/UNIV_SM-Profile_1600x1600px-scaled.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"2560\" \/>\n\t<meta property=\"og:image:height\" content=\"2560\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.uni.lu\/fr\/events\/from-thurstons-corrugations-to-smooth-fractals\/\",\"url\":\"https:\/\/www.uni.lu\/fr\/events\/from-thurstons-corrugations-to-smooth-fractals\/\",\"name\":\"From Thurston's Corrugations to Smooth Fractals - 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