{"id":6229,"date":"2026-06-25T14:34:55","date_gmt":"2026-06-25T05:34:55","guid":{"rendered":"https:\/\/www.ibs.re.kr\/ecopro\/?page_id=6229"},"modified":"2026-06-25T14:38:01","modified_gmt":"2026-06-25T05:38:01","slug":"summer-2026","status":"publish","type":"page","link":"https:\/\/www.ibs.re.kr\/ecopro\/summer-2026\/","title":{"rendered":"Summer 2026"},"content":{"rendered":"\n<ul id=\"block-5ee26a2a-7c74-446e-be1a-e5066c1642b7\" class=\"wp-block-list\">\n<li>Time: 9:00-10:30am (Beijing), 10:00-11:30am(Seoul)<\/li>\n\n\n\n<li>Place: <em>IBS ECOPRO <strong>B332<\/strong> (Main building 3rd floor).<\/em><\/li>\n\n\n\n<li><strong>Jul 6 &#8211; <strong>Jul <\/strong>10<\/strong>, Entropy method in extremal combinatorics<\/li>\n\n\n\n<li><strong><strong>Jul 27 &#8211; <strong>Jul <\/strong>31<\/strong><\/strong>, Hypergraphs with Bounded VC-Dimension: Incidences, Zarankiewicz Problems, and Radon-Type Theorems<\/li>\n\n\n\n<li><strong>Zoom: 3469344087, PW: 2026<\/strong><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><br>Entropy method in extremal combinatorics<\/h2>\n\n\n\n<h5 class=\"wp-block-heading\">Ting-Wei Chao,  Massachusetts Institute of Technology<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\"><em>The entropy method has been used in many recent works in extremalcombinatorics. With the help of Shannon entropy, significant progresshas been made on several classical problems, such as the union-closed conjecture and Sidorenko&#8217;s conjecture. There are also recent new proofs of classic theorems and their generalizations using entropy, such as the Kruskal-Katona theorem and Turan&#8217;s theorem. We will cover the basics of entropy and talk about some applications to graph homomorphism counting problems.<\/em><\/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-47613d38-375a-44b8-a017-256797930ada\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2025\/08\/IBS_2025Summer_removal_lemma.pdf\" 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: #cf2e2e; --ub-button-border: 3px solid #cf2e2e; --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: 100px;; border-top-right-radius: 100px;; border-bottom-left-radius: 100px;; border-bottom-right-radius: 100px;; \">\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>Note<\/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=\"https:\/\/www.bilibili.com\/video\/BV1Hz87zyEQ6\/\" 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>\n\n\n<ul class=\"wp-block-list\">\n<li>7\/6 Lecture 1:  <span style=\"color: #ff6900;\" class=\"stk-highlight\"><strong>NOTE 1<\/strong><\/span><\/li>\n\n\n\n<li>7\/7 Lecture 2: &nbsp;<strong><span style=\"color: #ff6900;\" class=\"stk-highlight\">NOTE 2<\/span><\/strong><\/li>\n\n\n\n<li>7\/8 Lecture 3: &nbsp;<strong><span style=\"color: #ff6900;\" class=\"stk-highlight\">NOTE 3<\/span><\/strong><\/li>\n\n\n\n<li>7\/9 Lecture 4:  <strong><strong><span style=\"color: #ff6900;\" class=\"stk-highlight\">NOTE 4<\/span><\/strong><\/strong><\/li>\n\n\n\n<li>7\/10 Lecture 5: &nbsp;<strong><span style=\"color: #ff6900;\" class=\"stk-highlight\">NOTE 5<\/span><\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><br>Hypergraphs with Bounded VC-Dimension: Incidences, Zarankiewicz Problems, and Radon-Type Theorems<\/h2>\n\n\n\n<h5 class=\"wp-block-heading\">Shakhar Smorodinsky, Ben-Gurion University<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\"><em>The notion of VC-dimension, introduced in statistical learning theory, has become a central tool inmodern combinatorics, discrete geometry, and theoretical computer science. It provides a powerful way to measure the complexity of set systems, or equivalently hypergraphs, and many natural geometric hypergraphs have bounded VC-dimension. In this course, I will discuss the rich combinatorial theory of hypergraphs with bounded VC-dimension and some of its geometric manifestations. We will begin with the Sauer-Shelah-Perles lemma and its basic consequences and then move to epsilon-nets and related sampling and packing phenomena. We will studyextremal questions for graphs and hypergraphs of bounded VC-dimension, including Zarankiewicz-type problems and incidence bounds, together with tools such as the crossing lemma and polynomial partitioning. Further topics will include matchings with low crossing numbers, generalizations of epsilon-nets, and Radon- and Tverberg-type theorems for unions of convex sets.<\/em><\/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-8484f513-95bd-4e1e-b774-fb65940e1f64\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2025\/08\/IBS_2025Summer_removal_lemma.pdf\" 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: #cf2e2e; --ub-button-border: 3px solid #cf2e2e; --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: 100px;; border-top-right-radius: 100px;; border-bottom-left-radius: 100px;; border-bottom-right-radius: 100px;; \">\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>Note<\/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=\"https:\/\/www.bilibili.com\/video\/BV1Hz87zyEQ6\/\" 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>\n\n\n<ul class=\"wp-block-list\">\n<li>7\/27 Lecture 1: <span style=\"color: #ff6900;\" class=\"stk-highlight\"><strong>NOTE 1<\/strong><\/span><\/li>\n\n\n\n<li>7\/28 Lecture 2: &nbsp;<strong><span style=\"color: #ff6900;\" class=\"stk-highlight\">NOTE 2<\/span><\/strong><\/li>\n\n\n\n<li>7\/29 Lecture 3: &nbsp;<strong><span style=\"color: #ff6900;\" class=\"stk-highlight\">NOTE 3<\/span><\/strong><\/li>\n\n\n\n<li>7\/30 Lecture 4: <strong><strong><span style=\"color: #ff6900;\" class=\"stk-highlight\">NOTE 4<\/span><\/strong><\/strong><\/li>\n\n\n\n<li>7\/31 Lecture 5: &nbsp;<strong><span style=\"color: #ff6900;\" class=\"stk-highlight\">NOTE 5<\/span><\/strong><\/li>\n<\/ul>\n\n\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Entropy method in extremal combinatorics Ting-Wei Chao, Massachusetts Institute of Technology The entropy method has been used in many recent works in extremalcombinatorics. With the help of Shannon entropy, significant &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/summer-2026\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Summer 2026&#8221;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"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-6229","page","type-page","status-publish","hentry"],"featured_image_src":null,"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Summer 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\/summer-2026\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Summer 2026 - Extremal Combinatorics and Probability Group\" \/>\n<meta property=\"og:description\" content=\"Entropy method in extremal combinatorics Ting-Wei Chao, Massachusetts Institute of Technology The entropy method has been used in many recent works in extremalcombinatorics. 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With the help of Shannon entropy, significant &hellip; Continue reading \"Summer 2026\"","jetpack_sharing_enabled":true,"ticketed":false,"_links":{"self":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/wp-json\/wp\/v2\/pages\/6229","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ibs.re.kr\/ecopro\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ibs.re.kr\/ecopro\/wp-json\/wp\/v2\/comments?post=6229"}],"version-history":[{"count":2,"href":"https:\/\/www.ibs.re.kr\/ecopro\/wp-json\/wp\/v2\/pages\/6229\/revisions"}],"predecessor-version":[{"id":6234,"href":"https:\/\/www.ibs.re.kr\/ecopro\/wp-json\/wp\/v2\/pages\/6229\/revisions\/6234"}],"wp:attachment":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/wp-json\/wp\/v2\/media?parent=6229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}