{"id":2595,"date":"2022-03-29T00:59:38","date_gmt":"2022-03-29T04:59:38","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2022\/?p=2595"},"modified":"2022-01-17T17:47:21","modified_gmt":"2022-01-17T22:47:21","slug":"lecture-18-the-laplace-beltrami-operator","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2022\/2022\/03\/29\/lecture-18-the-laplace-beltrami-operator\/","title":{"rendered":"Lecture 18: The Laplace-Beltrami Operator"},"content":{"rendered":"<p><a href=\"https:\/\/www.youtube.com\/watch?v=oEq9ROl9Umk\"><img loading=\"lazy\" src=\"http:\/\/brickisland.net\/DDGSpring2021\/wp-content\/uploads\/2020\/04\/DDG_458_SP20_Lecture18_LaplaceOperator.jpg\" alt=\"\" width=\"512\" height=\"288\" \/><\/a><\/p>\n<p>In this lecture we take a close look at the Laplacian, and its generalization to curved spaces via the <em>Laplace-Beltrami operator<\/em>. The Laplacian is one of the most fundamental objects in geometry and physics, and which plays a major role in algorithms.  Here we consider several perspectives to build up some basic intuition about what the Laplacian is, and what it means.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=oEq9ROl9Umk\">Video<\/a><\/li>\n<li><a href=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2020\/04\/DDG_458_SP20_Lecture18_LaplaceOperator.pdf\">Slides<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In this lecture we take a close look at the Laplacian, and its generalization to curved spaces via the Laplace-Beltrami operator. The Laplacian is one of the most fundamental objects in geometry and physics, and which plays a major role in algorithms. Here we consider several perspectives to build up some basic intuition about what &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/2022\/03\/29\/lecture-18-the-laplace-beltrami-operator\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 18: The Laplace-Beltrami Operator&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[7,3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/2595"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/comments?post=2595"}],"version-history":[{"count":5,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/2595\/revisions"}],"predecessor-version":[{"id":3451,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/2595\/revisions\/3451"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/media?parent=2595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/categories?post=2595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/tags?post=2595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}