{"id":1618,"date":"2025-06-02T22:56:35","date_gmt":"2025-06-02T20:56:35","guid":{"rendered":"https:\/\/kleineberg.co.uk\/CTS-2025\/?post_type=mp-event&#038;p=1618"},"modified":"2025-06-02T23:04:47","modified_gmt":"2025-06-02T21:04:47","slug":"chris-bishop-recorded-lecture","status":"publish","type":"mp-event","link":"https:\/\/kleineberg.co.uk\/CTS-2025\/timetable\/event\/chris-bishop-recorded-lecture\/","title":{"rendered":"Chris Bishop (Link to recorded lecture)"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><a href=\"https:\/\/www.math.stonybrook.edu\/~bishop\/lectures\/Berlin.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Curves, Trees and Surfaces: Applications to Mappings and Meshes<\/a>,<\/h2>\n\n\n\n<p>I will show that any closed curve in plane is encoded by its medial axis, a tree consisting of the centers of all disks enclosed by the curve whose boundary hits the curve in at least two points. For a polygon this is a finite tree. The medial axis gives rise to the iota map from the curve to the unit circles, and this map extends to an 8-QC map of the interiors, independent of the curve. This is really a theorem about surfaces in hyperbolic 3-space: the iota map is extends to a conformal map of the dome of the curve to the unit disk, a fact due to Thurston, Sullivan, Epstein and Marden. We then discuss various applications, including fast numerical conformal mapping and optimal quad-meshing and triangulation of polygonal domains.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Zoom recording: <a href=\"https:\/\/www.math.stonybrook.edu\/~bishop\/lectures\/GMT20250530-133351_Recording_3840x2280.mp4\">https:\/\/www.math.stonybrook.edu\/~bishop\/lectures\/GMT20250530-133351_Recording_3840x2280.mp4<\/a><\/p>\n\n\n\n<p>Slides: <a href=\"https:\/\/www.math.stonybrook.edu\/~bishop\/lectures\/Berlin.pdf\">https:\/\/www.math.stonybrook.edu\/~bishop\/lectures\/Berlin.pdf<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Curves, Trees and Surfaces: Applications to Mappings and Meshes, I will show that any closed curve in plane is encoded by its medial axis, a tree consisting of the centers of all disks enclosed by the curve whose boundary hits the curve in at least two points. For a polygon this is a finite tree. [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","mp-event_category":[15],"mp-event_tag":[],"class_list":["post-1618","mp-event","type-mp-event","status-publish","hentry","mp-event_category-speaker","entry","mp-event-item"],"_links":{"self":[{"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/mp-event\/1618","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/mp-event"}],"about":[{"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/types\/mp-event"}],"author":[{"embeddable":true,"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/comments?post=1618"}],"wp:attachment":[{"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/media?parent=1618"}],"wp:term":[{"taxonomy":"mp-event_category","embeddable":true,"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/mp-event_category?post=1618"},{"taxonomy":"mp-event_tag","embeddable":true,"href":"https:\/\/kleineberg.co.uk\/CTS-2025\/wp-json\/wp\/v2\/mp-event_tag?post=1618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}