{"id":5775,"date":"2026-01-04T21:16:53","date_gmt":"2026-01-04T12:16:53","guid":{"rendered":"https:\/\/www.ibs.re.kr\/ecopro\/?page_id=5775"},"modified":"2026-01-28T19:17:33","modified_gmt":"2026-01-28T10:17:33","slug":"winter-2026","status":"publish","type":"page","link":"https:\/\/www.ibs.re.kr\/ecopro\/winter-2026\/","title":{"rendered":"Winter 2026"},"content":{"rendered":"\n<ul class=\"wp-block-list\">\n<li>Time: everyday Jan 19 to Jan 23, 2026, offline at IBS headquarter B332.<br>Online: <strong><span style=\"color: #0693e3;\" class=\"stk-highlight\">9:00-10:30am (Beijing)<\/span><\/strong>, <strong><span style=\"color: #0693e3;\" class=\"stk-highlight\">10:00-11:30am (Seoul)<\/span><\/strong>.<\/li>\n\n\n\n<li><strong><span style=\"color: #9b51e0;\" class=\"stk-highlight\">Zoom: 955 7502 7689, PW: 260119<\/span><\/strong><\/li>\n<\/ul>\n\n\n\n<p>This mini-course will serve as an introduction to cut problems in graphs and related topics. The course will begin by covering the basics of spectral graph theory, including the Alon\u2013Boppana theorem and the expander mixing lemma. We will then introduce some fundamental tools in the field, such as the Goemans\u2013Williamson algorithm, along with its applications to various types of max-cut problems in graphs and hypergraphs. Towards the end of the course, we will explore recent advancements in the area, which rely on more involved spectral properties of adjacency matrices.<\/p>\n\n\n\n<p><\/p>\n\n\n<div style=\"gap: 20px;\" class=\"align-button-center ub-buttons orientation-button-row ub-flex-wrap wp-block-ub-button\" id=\"ub-button-69f255d2-68f9-4b08-841e-7426f1d2f46f\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.bilibili.com\/video\/BV1EKkaBoEVX\/\" target=\"_blank\" rel=\"noopener noreferrer nofollow\" class=\"ub-button-block-main   ub-button-flex\" role=\"button\" style=\"--ub-button-background-color: transparent; --ub-button-color: #0693e3; --ub-button-border: 3px solid #0693e3; --ub-button-hover-color: #313131; --ub-button-hover-border: 3px solid #313131; font-size: 17px; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-top-left-radius: 20%;; border-top-right-radius: 20%;; border-bottom-left-radius: 20%;; border-bottom-right-radius: 20%;; \">\n\t\t\t\t<div class=\"ub-button-content-holder\" style=\"flex-direction: row\">\n\t\t\t\t\t<span class=\"ub-button-block-btn\"><strong>Videos<\/strong><\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><div class=\"ub-button-container\">\n\t\t\t<a href=\"http:\/\/1\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"ub-button-block-main   ub-button-flex\" role=\"button\" style=\"--ub-button-background-color: #cf2e2e; --ub-button-color: #ffffff; --ub-button-border: none; --ub-button-hover-background-color: #313131; --ub-button-hover-color: #ffffff; --ub-button-hover-border: none; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-top-left-radius: 20px;; border-top-right-radius: 20px;; border-bottom-left-radius: 20px;; border-bottom-right-radius: 20px;; \">\n\t\t\t\t<div class=\"ub-button-content-holder\" style=\"flex-direction: row\">\n\t\t\t\t\t<span class=\"ub-button-block-btn\"><strong>YouTube<\/strong><\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>1\/19 <strong>Lecture 1<\/strong>: The max-cut problem, Edwards&#8217; bound and the expander mixing lemma. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/4399_001.pdf\"><span style=\"color: #0f0e17;\" class=\"stk-highlight\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Tablet note<\/mark><\/span><\/a><\/strong><\/li>\n\n\n\n<li>1\/20 <strong>Lecture 2<\/strong>: Alon-Boppana theorem and introduction to graph&nbsp;discrepancy. <strong><span style=\"color: #0f0e17;\" class=\"stk-highlight\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/4403_001.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Tablet note<\/mark><\/a><\/span><\/strong><\/li>\n\n\n\n<li>1\/21 <strong>Lecture 3<\/strong>: Bollob\u00e1s-Scott inverse relation between positive and negative discrepancy, and Goemans-Williamson method. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/0022_001.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Tablet note<\/mark><\/a><\/strong><\/li>\n\n\n\n<li>1\/22 <strong>Lecture 4<\/strong>: Optimal surplus for triangle-free graphs, and improved&nbsp;lower bounds for positive discrepancy of sparse graphs.&nbsp; <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/0027_001.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Tablet note<\/mark><\/a><\/strong><\/li>\n\n\n\n<li>.1\/23 <strong>Lecture 5<\/strong>: Lower bounds for the second largest eigenvalue and positive discrepancy when p &lt; 1\/2. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/0028_001.pdf\" type=\"link\" id=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/0028_001.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Tablet note<\/mark><\/a><\/strong> \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/references-1.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\"><strong>Reference list\u00a0<\/strong><\/mark><\/a><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-stackable-image stk-block-image stk-block stk-8c471ef\" data-block-id=\"8c471ef\"><figure><span class=\"stk-img-wrapper stk-image--shape-stretch\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-5776\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/f43ebfe0783320e907666529f13c7e08.jpg\" width=\"1280\" height=\"1811\" srcset=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/f43ebfe0783320e907666529f13c7e08.jpg 1280w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/f43ebfe0783320e907666529f13c7e08-212x300.jpg 212w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/f43ebfe0783320e907666529f13c7e08-724x1024.jpg 724w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/f43ebfe0783320e907666529f13c7e08-768x1087.jpg 768w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/f43ebfe0783320e907666529f13c7e08-1086x1536.jpg 1086w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/f43ebfe0783320e907666529f13c7e08-283x400.jpg 283w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/span><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"<p>This mini-course will serve as an introduction to cut problems in graphs and related topics. The course will begin by covering the basics of spectral graph theory, including the Alon\u2013Boppana &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/winter-2026\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Winter 2026&#8221;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":5776,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_uag_custom_page_level_css":"","_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":"","_tec_slr_enabled":"","_tec_slr_layout":""},"class_list":["post-5775","page","type-page","status-publish","has-post-thumbnail","hentry"],"featured_image_src":"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2026\/01\/f43ebfe0783320e907666529f13c7e08.jpg","yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Winter 2026 - Extremal Combinatorics and Probability Group<\/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:\/\/www.ibs.re.kr\/ecopro\/winter-2026\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Winter 2026 - Extremal Combinatorics and Probability Group\" \/>\n<meta property=\"og:description\" content=\"This mini-course will serve as an introduction to cut problems in graphs and related topics. 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