{"id":1256,"date":"2019-03-01T10:32:38","date_gmt":"2019-03-01T18:32:38","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=1256"},"modified":"2019-04-18T11:42:15","modified_gmt":"2019-04-18T18:42:15","slug":"ccms-colloquium-kao-cmc","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/ccms-colloquium-kao-cmc\/","title":{"rendered":"A Conformal Mapping Approach to Shape Optimization Problems. (Kao, CMC)"},"content":{"rendered":"<p>Abstract: In this talk, a conformal mapping approach to shape optimization problems on planar domains will be discussed. In particular,\u00a0spectral methods based on conformal mappings are proposed to solve Steklov eigenvalues and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov eigenvalue problem in the complex domain via conformal mappings. The eigenfunctions are expanded in Fourier series so the discretization leads to an eigenvalue problem for coefficients of Fourier series. For shape optimization problems, we use gradient ascent approaches to find optimal domains that maximize objective functions involving Steklov eigenvalues.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Abstract: In this talk, a conformal mapping approach to shape optimization problems on planar domains will be discussed. In particular,\u00a0spectral methods based on conformal mappings are proposed to solve Steklov [&hellip;]<\/p>\n","protected":false},"author":79,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":""},"tags":[],"tribe_events_cat":[12],"class_list":["post-1256","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-colloquium","cat_colloquium"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>A Conformal Mapping Approach to Shape Optimization Problems. (Kao, CMC) - Claremont Center for the Mathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/colleges.claremont.edu\/ccms\/event\/ccms-colloquium-kao-cmc\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A Conformal Mapping Approach to Shape Optimization Problems. (Kao, CMC) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Abstract: In this talk, a conformal mapping approach to shape optimization problems on planar domains will be discussed. In particular,\u00a0spectral methods based on conformal mappings are proposed to solve Steklov [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/ccms-colloquium-kao-cmc\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2019-04-18T18:42:15+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/ccms-colloquium-kao-cmc\\\/\",\"url\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/ccms-colloquium-kao-cmc\\\/\",\"name\":\"A Conformal Mapping Approach to Shape Optimization Problems. 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