{"id":4323,"date":"2024-02-14T09:58:27","date_gmt":"2024-02-14T00:58:27","guid":{"rendered":"https:\/\/www.ibs.re.kr\/ecopro\/?page_id=4323"},"modified":"2024-09-13T23:25:22","modified_gmt":"2024-09-13T14:25:22","slug":"spring-2024","status":"publish","type":"page","link":"https:\/\/www.ibs.re.kr\/ecopro\/spring-2024\/","title":{"rendered":"Spring 2024"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n<h1 class=\"wp-block-heading\"><span style=\"color: #cf2e2e;\" class=\"stk-highlight\"><strong>Extremal Combinatorics I<\/strong><\/span><\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Time: From March 5th till June 13th, 2024, every Tuesday and Thursday<br><strong><span style=\"color: #0693e3;\" class=\"stk-highlight\">8:30-10:00am (Beijing)<\/span><\/strong>, <strong><span style=\"color: #0693e3;\" class=\"stk-highlight\">9:30-11:00am(Seoul)<\/span><\/strong>.<\/li>\n\n\n\n<li><strong><span style=\"color: #9b51e0;\" class=\"stk-highlight\">Zoom: 346 934 4087, PW: 202402<\/span><\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><span style=\"background-color: #7bdcb5\" class=\"stk-highlight\">Final exam<\/span><\/h4>\n\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-b61a3ded-8d86-41a1-b744-0d0f6686ec15\" data-mobilecollapse=\"false\" data-desktopcollapse=\"true\" data-preventcollapse=\"false\" data-showonlyone=\"false\">\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-4e0b1fc5-23f3-4f98-83f2-f8a225ac8fe9\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-0-b61a3ded-8d86-41a1-b744-0d0f6686ec15\" tabindex=\"0\">\n\t\t\t<p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b61a3ded-8d86-41a1-b744-0d0f6686ec15\" style=\"color: #000000; \">Final Exam information<\/p>\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap left\" style=\"color: #000000;\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span><\/div>\n\t\t<\/div>\n\t\t\t<div role=\"region\" aria-expanded=\"false\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-b61a3ded-8d86-41a1-b744-0d0f6686ec15\">\n\n<ul class=\"wp-block-list\">\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">If you wish to take the final, please register. <\/span><\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">How to register: send an email with title &#8220;ECOPRO-Spring2024-Name+University&#8221; to Z&#104;&#x75;&#x6f;&#46;&#87;&#x75;&#x40;w&#97;&#114;&#x77;&#x69;c&#107;&#x2e;&#x61;c&#46;&#x75;&#x6b;.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Deadline<\/mark>: 5\/21 mid-night everywhere in the world. <\/span><\/em><\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">Final exam will be on Saturday 5\/25 8:30-11:30am (Beijing), <strong><em>9:30am-12:30pm (Seoul)<\/em><\/strong>. <\/span><\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><strong><em><span style=\"color: #0e0e95;\" class=\"stk-highlight\">It is an online exam, hosted on the same zoom: <strong>346 934 4087, PW: 202402<\/strong><\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">When entering the zoom, please change id to:  &#8220;Name + University&#8221;<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">The zoom room will be open 20 minutes before the exam. Please make sure to enter before 8:30am (Beijing)=9:30am (Seoul). No late admission is allowed.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">The final exam problem sheet will be posted 10 minutes before the exam via a link in the zoom chat.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">Please take the exam using our designated answer sheet. You can download and print out the answer sheet beforehand. <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/05\/answer-sheet.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Download Answer Sheet<\/mark><\/a><\/span><\/em><\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">Examinable material: Lecture 1 &#8212; Lecture 21.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">Exam rules. During the online exam, please adhere to the following rules, otherwise it will be considered cheating.<\/span><\/em><\/strong>\n<ul class=\"wp-block-list\">\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">This is a closed book exam. Do not place textbooks, exercise books, or any irrelevant materials on the desk. <\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">Prepare two devices to log in zoom (laptop+phone) both with the same id &#8220;Name+Uni&#8221;.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">Turn on the cameras on your phone and computer at the same time. While the computer&#8217;s camera is facing the test taker, place the phone camera on the side, about 50-100cm away, so that the test taker&#8217;s face, hands, and desk surface are clearly visible. Keep the Zoom video on your phone active during the exam.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">Keep your computer from going to sleep or activating screen savers. During the exam, you are not allowed to operate the computer or phone. <\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">At the end of the exam, take photos of the answer sheets with your phone, then merge them into a PDF file (you can use scanning apps like &#8220;Scanner Pro&#8221;). Please make sure to send the PDF file to <strong><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">Zh&#117;&#111;&#46;&#87;&#x75;&#x40;&#x77;&#x61;&#x72;wi&#99;&#107;&#46;&#97;&#x63;&#x2e;&#x75;&#x6b;<\/span><\/em><\/strong><\/strong> within 10 minutes after the exam. No late submission will be allowed. If it&#8217;s not convenient to merge the sheets into a PDF, you can directly send the numbered images to the invigilator. <\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #0f0e97;\" class=\"stk-highlight\">Zoom and device testing. We will open the same zoom on 5\/24 Friday 7:30-7:50pm Beijing = 8:30-8:50pm Seoul evening if you wish to check your cameras and other devices.<\/span><\/em><\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\"><span style=\"color: #222222;background-color: #ff6900\" class=\"stk-highlight\">Announcement<\/span><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><em><span style=\"color: #cf2e2e;\" class=\"stk-highlight\">The last two classes on 6\/11 &amp; 6\/13 will be at 13:30-15:00 (Beijing), <strong>14:30-16:00pm<\/strong> (Seoul).<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #cf2e2e;\" class=\"stk-highlight\">There will be a summer research program at ECOPRO in July and August of this year.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #abb8c3;\" class=\"stk-highlight\">The Thursday class on June 6 will be switched to the same time on Friday June 7.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #abb8c3;\" class=\"stk-highlight\">The Tuesday class on June 4 will be switched to the same time on Monday June 3.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><span style=\"color: #abb8c3;\" class=\"stk-highlight\">There is no class on Thursday 5\/23.<\/span><\/mark><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #abb8c3;\" class=\"stk-highlight\">There is no class on Thursday 5\/2.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #abb8c3;\" class=\"stk-highlight\">The Tuesday class on 4\/16 will be switched to the same time on Monday April 15.<\/span><\/em><\/strong><\/li>\n\n\n\n<li><strong><em><span style=\"color: #abb8c3;\" class=\"stk-highlight\">The class on 3\/12 will be at 10am-11:30am (Beijing), <strong>11am-12:30pm<\/strong> (Seoul).<\/span><\/em><\/strong><\/li>\n<\/ul>\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-0b398f6f-58df-4971-838b-580969d4cf66\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.overleaf.com\/read\/cgrmhknxqsct#8e49cc\" 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: #fcb900; --ub-button-border: 3px solid #fcb900; --ub-button-hover-color: #313131; --ub-button-hover-border: 3px solid #313131; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-top-left-radius: 30px;; border-top-right-radius: 30px;; border-bottom-left-radius: 30px;; border-bottom-right-radius: 30px;; \">\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\/BV12x42127DR\/\" 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; 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=\"https:\/\/www.youtube.com\/watch?v=ejKB8fyXpWE&amp;list=PL1GwqxNoajg0GNgAfpRIcgfUYGgEIdnUn\" 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<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Final grade: Homeworks 50%, exam 50%. Please send homework to Zh&#117;&#111;&#46;&#x57;&#x75;&#x40;&#x77;ar&#119;&#105;&#99;&#x6b;&#x2e;&#x61;&#x63;&#46;u&#107;<\/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-ae147360-5656-41d3-a419-9519d04db440\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/HW-1.pdf\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"ub-button-block-main   ub-button-flex\" role=\"button\" style=\"--ub-button-background-color: #313131; --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: 10px;; border-top-right-radius: 10px;; border-bottom-left-radius: 10px;; border-bottom-right-radius: 10px;; \">\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\">HW 1<\/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.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/HW-2.pdf\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"ub-button-block-main   ub-button-flex\" role=\"button\" style=\"--ub-button-background-color: #313131; --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: 10px;; border-top-right-radius: 10px;; border-bottom-left-radius: 10px;; border-bottom-right-radius: 10px;; \">\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\">HW 2<\/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.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/05\/HW-3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\" class=\"ub-button-block-main   ub-button-flex\" role=\"button\" style=\"--ub-button-background-color: #313131; --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: 10px;; border-top-right-radius: 10px;; border-bottom-left-radius: 10px;; border-bottom-right-radius: 10px;; \">\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\">HW 3<\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>\n\n\n<h2 class=\"wp-block-heading has-text-align-center\"><strong><span style=\"color: #0693e3;\" class=\"stk-highlight\">Part 1. Topics<\/span><\/strong><\/h2>\n\n\n\n<div class=\"wp-block-stackable-image stk-block-image stk-block stk-73463a2\" data-block-id=\"73463a2\"><style>.stk-73463a2{margin-bottom:0px !important}.stk-73463a2 .stk-img-wrapper{filter:drop-shadow(none) !important}.stk-73463a2 .stk-img-wrapper img{border-radius:25px !important}<\/style><figure><span class=\"stk-img-wrapper stk-image--shape-stretch stk--shadow-none\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-4522\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/turan-1.png\" width=\"1974\" height=\"1150\" srcset=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/turan-1.png 1974w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/turan-1-300x175.png 300w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/turan-1-1024x597.png 1024w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/turan-1-768x447.png 768w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/turan-1-1536x895.png 1536w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/turan-1-600x350.png 600w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/span><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>1. <span style=\"color: #cf2e2e;\" class=\"stk-highlight\">Tur\u00e1n problem<\/span><\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3\/5 <strong>Lecture 1<\/strong>: graph, handshaking lemma, common graph families, subgraph, large degree \u21d2 long cycle &amp; large trees, Mantel&#8217;s thm, pf1 induction, pf2 max-deg vertex, odd\/even town via linear algebra, lower bd construction for Ramsey via probabilistic method. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/Lecture-1.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>3\/7 <strong>Lecture 2<\/strong>: Erd\u0151s-Szekeres monotone seq via pigeonhole, Sperner&#8217;s thm via LYM ineq, pf1 double counting, pf2 probabilistic counting, extremal number, Tur\u00e1n graph, Tur\u00e1n&#8217;s thm, pf1 induction, pf2 max-deg vertex, pf3 Zykov&#8217;s symmetrization. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/Lecture-2.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>3\/12 <strong>Lecture 3<\/strong>: Tur\u00e1n&#8217;s thm, pf4 Motzkin-Straus Symmetrization, pf5 probabilistic pf Caro-Wei, first moment method, Erd\u0151s-Stone-Simonovits thm pf1. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/Lecture-3.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>3\/14 <strong>Lecture 4<\/strong>: a geometric application of Tur\u00e1n&#8217;s thm, homomorphism, an embedding lemma bootstrapping $H$-freeness to $H$-hom-freeness, a modern pf2 of Erd\u0151s-Stone-Simonovits thm, supersaturation phenomenon, Tur\u00e1n density exists for every graph. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/Lecture-4.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>3\/19 <strong>Lecture 5<\/strong>: $r$-uniform $r$-partite hypergraph has Tur\u00e1n density 0, supersaturation pf1 local averaging, supersaturation \u21d2 blowups of a graph has the same Tur\u00e1n density \u21d2 pf3 Erd\u0151s-Simonovits-Stone, Moon-Moser \u21d2 supersaturation pf2. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/Lecture-5.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>3\/21 <strong>Lecture 6<\/strong>: F\u00fcredi perfect stability via degree majorization, Erd\u0151s-Simonovits stability from perfect stability and Ruzsa-Szemer\u00e9di removal lemma, stability method. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/Lecture-6.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>3\/26 <strong>Lecture 7<\/strong>: extremal number of $C_5$ via stability, every maximal $K_r$-free graph contains a wheel-like graph, Brandt&#8217;s pf of Andrasfai-Erd\u0151s-S\u00f3s. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/Lecture-7.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>3\/28 <strong>Lecture 8<\/strong>: Bipartite Tur\u00e1n problem, $C_4$ and Sidon-set, K\u0151v\u00e1ri-S\u00f3s-Tur\u00e1n, dense constructions of $C_4$-free and $K_{3,3}$-free graphs, Bondy-Simonovits on extremal number of even cycles, pf1 using BFS. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/03\/Lecture-8.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>4\/2 <strong>Lecture 9<\/strong>: Regularization, bipartite graph with bounded degree, random zooming. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/Lecture-9.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>4\/4 <strong>Lecture 10<\/strong>: Sidorenko&#8217;s conjecture, $P_3, C_4$, even cycles, pf2 of even cycle extremal number upper bound using Sidorenko. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/Lecture-10.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>4\/9 <strong>Lecture 11<\/strong>: 3-dim cube via supersaturation, grid via rich collection of paths, pf3 of even cycle via Sidorenko and iterative Cauchy-Schwarz. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/Lecture-11.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/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-08d003c\" data-block-id=\"08d003c\"><style>.stk-08d003c .stk-img-wrapper img{border-radius:25px !important}<\/style><figure><span class=\"stk-img-wrapper stk-image--shape-stretch\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-4524\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/intersection.png\" width=\"1944\" height=\"1266\" srcset=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/intersection.png 1944w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/intersection-300x195.png 300w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/intersection-1024x667.png 1024w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/intersection-768x500.png 768w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/intersection-1536x1000.png 1536w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/intersection-600x391.png 600w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/span><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>2. Extremal Set Theory<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4\/11 <strong>Lecture 12<\/strong>: Bollob\u00e1s set-pairs ineq, pf via random permutation, skewed version via exterior algebra, applications: 1. LYM ineq, 2. saturation number. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/Lecture-12.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>4\/15 <strong>Lecture 13<\/strong>: Application of Sperner: Littlewood-Offord, Poset, height, width, Dilworth&#8217;s thm, pf1 induction, Mirsky&#8217;s thm. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/Lecture-13.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>4\/18 <strong>Lecture 14<\/strong>: Dilworth pf2 symm chain decomposition, pf3 K\u0151nig&#8217;s thm, Application of Dilworth: better Ramsey for interval graphs and intersection graphs of planar convex sets. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/Lecture-14.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>4\/23 <strong>Lecture 15<\/strong>: Ramsey for intersection graph of rectangles in the plane via Dilworth, Erd\u0151s-Rado&#8217;s sunflower lemma. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/Lecture-15.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>4\/25 <strong>Lecture 16<\/strong>: Harris-Kleitman correlation inequality and applications on intersecting families. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/Lecture-16.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>4\/30 <strong>Lecture 17<\/strong>: Erd\u0151s-Ko-Rado, Katona&#8217;s pf, counting intersecting uniform families. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/Lecture-17.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>5\/7 <strong>Lecture 18<\/strong>: Counting maximal intersecting uniform families via Bollob\u00e1s set-pairs ineq, colexicographic order, shadow, Kruskal-Katona. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/05\/Lecture-18.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>5\/9 <strong>Lecture 19<\/strong>: Pf Kruskal-Katona via shifting, VC dimension. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/05\/Lecture-19.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>5\/14 <strong>Lecture 20<\/strong>: 3 pfs of Sauer-Shelah, Dimension argument. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/05\/Lecture-20.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>5\/16 <strong>Lecture 21<\/strong>: De Bruijn-Erd\u0151s, sets with at most two distinct distances, Frankl-Wilson forbidding a single intersection size. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/05\/Lecture-21.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>5\/21 <strong>Lecture 22<\/strong>: Application of Frankl-Wilson: sets with no orthogonal pairs, Kahn-Kalai on Borsuk&#8217;s conjecture, Katona&#8217;s intersection thm. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/05\/Lecture-22.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/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-b3edbd4\" data-block-id=\"b3edbd4\"><style>.stk-b3edbd4 .stk-img-wrapper img{border-radius:0px !important}<\/style><figure><span class=\"stk-img-wrapper stk-image--shape-stretch\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-4679\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/partition.png\" width=\"1024\" height=\"1024\" srcset=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/partition.png 1024w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/partition-300x300.png 300w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/partition-150x150.png 150w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/partition-768x768.png 768w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/partition-400x400.png 400w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/partition-100x100.png 100w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/span><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>3. Szemer\u00e9di&#8217;s Regularity Lemma<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5\/28 <strong>Lecture 23<\/strong>: Regular pair, regular partition, Szemer\u00e9di&#8217;s regularity lemma, slicing lemma, reduced graph. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/05\/Lecture-23.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>5\/30 <strong>Lecture 24<\/strong>: Embedding lemma, counting lemma, Ramsey-Tur\u00e1n for $K_4$. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/Lecture-24.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>6\/3 <strong>Lecture 25<\/strong>: Multicolor regularity lemma, Chv\u00e1tal-R\u00f6dl-Szemer\u00e9di-Trotter bdd deg graph Ramsey number linear, Ruzsa-Szemer\u00e9di triangle removal lemma. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/Lecture-25.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>6\/7 <strong>Lecture 26<\/strong>: Triangle removal lemma \u21d2 (6,3)-thm \u21d2 Roth&#8217;s thm, Induced matching thm \u21d2 (6,3)-thm. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/Lecture-26.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>6\/11 <strong>Lecture 27<\/strong>: Pf induced matching thm, pts\/lines incidence graphs, Matou\u0161ek&#8217;s cutting lemma. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/Lecture-27.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li>\n\n\n\n<li>6\/13 <strong>Lecture 28<\/strong>: Application of removal lemma on $C_6$-free pts\/lines incidence graph, Regularity lemma as containers, counting $K_{r+1}$-free graphs on $[n]$, linear-size clique in dense graphs with no induced $C_4$. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/06\/Lecture-28.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/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-b509fbb\" data-block-id=\"b509fbb\"><figure><span class=\"stk-img-wrapper stk-image--shape-stretch\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-4335\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/02\/spring2024course.jpg\" width=\"742\" height=\"1112\" srcset=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/02\/spring2024course.jpg 742w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/02\/spring2024course-200x300.jpg 200w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/02\/spring2024course-683x1024.jpg 683w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/02\/spring2024course-267x400.jpg 267w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/span><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Extremal Combinatorics I Final exam Announcement Final grade: Homeworks 50%, exam 50%. Please send homework to &#x5a;h&#x75;&#111;&#x2e;&#87;&#x75;&#x40;w&#x61;&#114;&#x77;&#105;&#x63;&#107;&#46;&#x61;&#99;&#x2e;&#117;&#x6b; Part 1. Topics 1. Tur\u00e1n problem 2. Extremal Set Theory 3. Szemer\u00e9di&#8217;s Regularity &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/spring-2024\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Spring 2024&#8221;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":4516,"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-4323","page","type-page","status-publish","has-post-thumbnail","hentry"],"featured_image_src":"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/04\/graph.png","yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Spring 2024 - 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\/spring-2024\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Spring 2024 - Extremal Combinatorics and Probability Group\" \/>\n<meta property=\"og:description\" content=\"Extremal Combinatorics I Final exam Announcement Final grade: Homeworks 50%, exam 50%. 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