{"id":2211,"date":"2026-08-20T11:21:09","date_gmt":"2026-08-20T15:21:09","guid":{"rendered":"https:\/\/jasoncantarella.com\/wordpress\/?page_id=2211"},"modified":"2026-08-27T10:39:58","modified_gmt":"2026-08-27T14:39:58","slug":"ddg","status":"publish","type":"page","link":"https:\/\/jasoncantarella.com\/wordpress\/courses\/ddg\/","title":{"rendered":"MATH 8230: Continuous and Discrete Differential Geometry"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">This course, taught in Fall 2026, is a very idiosyncratic and personal spin on <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/\">Keenan Crane&#8217;s &#8220;Discrete Differential Geometry&#8221; course<\/a> for an audience of mathematics graduate students. The idea of the course is to fill in a lot of the differential geometry theory that&#8217;s mentioned in Crane but not explored and also to connect the ideas in the course not just to algorithms but to theorems in the pl category; a sort of synthesis of computational geometry and more analytic differential geometry techniques.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The <a href=\"https:\/\/www.jasoncantarella.com\/downloads\/CantarellaJ_MATH8230_Fall2026.pdf\">syllabus is here<\/a>. Unusually for a graduate course, there is (optional) homework, assigned on <a href=\"https:\/\/www.gradescope.com\">Gradescope<\/a> (ask me in class for the course entry code). I&#8217;ll post some lecture notes and papers on this page, along with Mathematica demonstration notebooks for you to play with. The textbook is Crane&#8217;s <a href=\"https:\/\/www.cs.cmu.edu\/~kmcrane\/Projects\/DDG\/paper.pdf\">Discrete Differential Geometry: An Applied Introduction<\/a>. The notes are quite rough and contain many errors.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.jasoncantarella.com\/downloads\/DCRG_polylines_curve_shortening.pdf\">Discrete curvatures for plane polylines and curve shortening flow<\/a>.\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/arxiv.org\/pdf\/0908.2682\">Curvature Bound for Curve Shortening Flow via Distance Comparison and a Direct Proof of Grayson&#8217;s Theorem. Andrews and Bryan, 2011. <\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.jasoncantarella.com\/downloads\/LengthPreservingFlow.nb\">Mathematica demonstration of the Andrews-Bryan flow (and theorem).<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This course, taught in Fall 2026, is a very idiosyncratic and personal spin on Keenan Crane&#8217;s &#8220;Discrete Differential Geometry&#8221; course for an audience of mathematics graduate students. The idea of the course is to fill in a lot of the differential geometry theory that&#8217;s mentioned in Crane but not explored and also to connect the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":78,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2211","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/2211","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/comments?post=2211"}],"version-history":[{"count":6,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/2211\/revisions"}],"predecessor-version":[{"id":2226,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/2211\/revisions\/2226"}],"up":[{"embeddable":true,"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/pages\/78"}],"wp:attachment":[{"href":"https:\/\/jasoncantarella.com\/wordpress\/wp-json\/wp\/v2\/media?parent=2211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}