{"id":238,"date":"2025-12-26T16:20:30","date_gmt":"2025-12-26T08:20:30","guid":{"rendered":"https:\/\/www.math.ntnu.edu.tw\/coidap\/?p=238"},"modified":"2026-01-05T14:14:43","modified_gmt":"2026-01-05T06:14:43","slug":"%e5%b0%88%e9%a1%8c%e6%bc%94%e8%ac%9b-%e3%80%909%e6%9c%8810%e6%97%a5%e3%80%91kai-hsiang-wang-optimal-transport-and-two-proofs-of-isoperimetric-inequality","status":"publish","type":"post","link":"https:\/\/www.math.ntnu.edu.tw\/coidap\/2025\/12\/26\/%e5%b0%88%e9%a1%8c%e6%bc%94%e8%ac%9b-%e3%80%909%e6%9c%8810%e6%97%a5%e3%80%91kai-hsiang-wang-optimal-transport-and-two-proofs-of-isoperimetric-inequality\/","title":{"rendered":"<span style=\"color:#3566BD\">[\u5c08\u984c\u6f14\u8b1b] <\/span>\u30109\u670810\u65e5\u3011Kai-Hsiang Wang \/ Optimal Transport and Two Proofs of Isoperimetric Inequality"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"238\" class=\"elementor elementor-238\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4708bf5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4708bf5\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7721725f\" data-id=\"7721725f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-233bb8b4 elementor-widget elementor-widget-heading\" data-id=\"233bb8b4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Optimal Transport and Two Proofs of Isoperimetric Inequality<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ed82028 elementor-widget elementor-widget-spacer\" data-id=\"6ed82028\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7f54a6f4 elementor-widget elementor-widget-text-editor\" data-id=\"7f54a6f4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><strong><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal;\">Time:<\/span><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal;\"> Sep. 10<\/span><\/strong><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: bold;\"> (Wed.) 14:20-15:10<br \/><\/span><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: bold;\">Venue: M212, Gongguan Campus, NTNU<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1d2118fb elementor-widget__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"1d2118fb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 22px; line-height: 26px; text-align: center; color: #cc6633; font-weight: bold;\"><p>Dr. Kai-Hsiang Wang<\/p><h4><span style=\"color: #ab7326;\">Visiting scholar of National Center for Theoretical Sciences<\/span><\/h4><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2e68c140 elementor-widget elementor-widget-spacer\" data-id=\"2e68c140\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1b3864a5 elementor-widget elementor-widget-text-editor\" data-id=\"1b3864a5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"color: #000000;\">In the first part of this talk, I will give an introduction to optimal transport (OT) theory, focusing on the Euclidean setting with the quadratic cost. This will include Kantorovich&#8217;s duality and Brenier&#8217;s theorem about OT maps. In the second part, I will give two structurally similar proofs of the classical isoperimetric inequality, one by the OT and the other by the ABP maximum principle.\u00a0<\/span><\/p><p><span style=\"color: #000000;\">More Information: <span style=\"text-decoration: underline;\"><a style=\"color: #000000; text-decoration: underline;\" href=\"https:\/\/k-hwang.github.io\/\" target=\"_blank\" rel=\"noopener\">https:\/\/k-hwang.github.io\/<\/a><\/span><\/span><\/p><p><em><u>Sponsored by &#8220;Higher Education Sprout Projec<\/u><\/em><em><u>t&#8221; of National Taiwa<\/u><\/em><em><u>n Normal University<\/u><\/em><img decoding=\"async\" class=\"wp-image-252 alignright\" src=\"https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/LOGO100-1-273x300.png\" alt=\"\" width=\"52\" height=\"57\" srcset=\"https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/LOGO100-1-273x300.png 273w, https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/LOGO100-1.png 326w\" sizes=\"(max-width: 52px) 100vw, 52px\" \/><img decoding=\"async\" class=\"wp-image-251 alignright\" src=\"https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/Center_logo_transparent-1-300x297.jpg\" alt=\"\" width=\"50\" height=\"50\" srcset=\"https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/Center_logo_transparent-1-300x297.jpg 300w, https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/Center_logo_transparent-1-150x150.jpg 150w, https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/Center_logo_transparent-1-600x600.jpg 600w, https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/Center_logo_transparent-1.jpg 645w\" sizes=\"(max-width: 50px) 100vw, 50px\" \/><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-530a75ea elementor-widget elementor-widget-image\" data-id=\"530a75ea\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1240\" height=\"758\" src=\"https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/\u6f14\u8b1b\u6a19\u5c3e.jpg\" class=\"attachment-full size-full wp-image-245\" alt=\"\" srcset=\"https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/\u6f14\u8b1b\u6a19\u5c3e.jpg 1240w, https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/\u6f14\u8b1b\u6a19\u5c3e-300x183.jpg 300w, https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/\u6f14\u8b1b\u6a19\u5c3e-1024x626.jpg 1024w, https:\/\/www.math.ntnu.edu.tw\/coidap\/wp-content\/uploads\/2025\/12\/\u6f14\u8b1b\u6a19\u5c3e-768x469.jpg 768w\" sizes=\"(max-width: 1240px) 100vw, 1240px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Optimal Transport and Two Proofs of Isoperimetric Inequ 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