{"id":98,"date":"2022-03-13T13:59:48","date_gmt":"2022-03-13T04:59:48","guid":{"rendered":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/?page_id=98"},"modified":"2025-11-17T14:49:29","modified_gmt":"2025-11-17T05:49:29","slug":"teaching","status":"publish","type":"page","link":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/teaching\/","title":{"rendered":"Teaching"},"content":{"rendered":"<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" data-mobilecollapse=\"true\" 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-\">\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-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Autumn 2024 Extremal Combinatorics II. Methods<\/h2>\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-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-extremal-combinatorics-and-probability-group wp-block-embed-extremal-combinatorics-and-probability-group\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"gsEk1pQcDZ\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/autumn-2024\/\">Autumn 2024<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cAutumn 2024\u201d \u2014 Extremal Combinatorics and Probability Group\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/autumn-2024\/embed\/#?secret=AhwiOeZLUz#?secret=gsEk1pQcDZ\" data-secret=\"gsEk1pQcDZ\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-beda1c8e-d4b0-44e8-8d1f-b24df27a0a0f\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-1-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Spring 2024 Extremal Combinatorics I. Topics<\/h2>\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-1-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-extremal-combinatorics-and-probability-group wp-block-embed-extremal-combinatorics-and-probability-group\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"5wvs0lyTmf\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/spring-2024\/\">Spring 2024<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cSpring 2024\u201d \u2014 Extremal Combinatorics and Probability Group\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/spring-2024\/embed\/#?secret=M9uK6P59Db#?secret=5wvs0lyTmf\" data-secret=\"5wvs0lyTmf\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-fcb35a4e-53f2-482b-b451-1dbd656c6268\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-2-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Autumn 2022 Topics in Extremal Combinatorics<\/h2>\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-2-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-extremal-combinatorics-and-probability-group wp-block-embed-extremal-combinatorics-and-probability-group\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"qmYyoGSWZf\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/autumn-2022\/\">Autumn 2022<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cAutumn 2022\u201d \u2014 Extremal Combinatorics and Probability Group\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/autumn-2022\/embed\/#?secret=NWmgzQYrH0#?secret=qmYyoGSWZf\" data-secret=\"qmYyoGSWZf\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-ee47e75c-eea4-4b1d-93d0-f99d8e46044c\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-3-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Summer 2022 Convexity space<\/h2>\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-3-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-extremal-combinatorics-and-probability-group wp-block-embed-extremal-combinatorics-and-probability-group\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"Ee0MwRtE2i\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/summer-2022\/\">Summer 2022<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cSummer 2022\u201d \u2014 Extremal Combinatorics and Probability Group\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/summer-2022\/embed\/#?secret=0ieQsatNJ2#?secret=Ee0MwRtE2i\" data-secret=\"Ee0MwRtE2i\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-732aaf8c-2fd1-4138-af94-b23b2a8bebab\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-4-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Spring 2022 Discrete geometry<\/h2>\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-4-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-extremal-combinatorics-and-probability-group wp-block-embed-extremal-combinatorics-and-probability-group\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"flOvQAsJoO\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/spring-2022\/\">Spring 2022<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cSpring 2022\u201d \u2014 Extremal Combinatorics and Probability Group\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/spring-2022\/embed\/#?secret=4cKYAsdMWZ#?secret=flOvQAsJoO\" data-secret=\"flOvQAsJoO\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-69ea28a6-a049-4bbc-915e-4abfd9895cb0\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-5-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Autumn 2021 Topics 2<\/h2>\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-5-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n<div style=\"gap: 20px;\" class=\"align-button-center ub-buttons orientation-button-row ub-flex-wrap wp-block-ub-button\" id=\"ub-button-c950fd40-ffc7-425e-8822-486819ed20c3\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/SDU2021-Fall.pdf\" target=\"_self\" 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; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-radius: 64px; \">\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\">Note<\/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\/BV17L411t7RP?p=1\" target=\"_self\" 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-radius: 46px; \">\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\">Videos<\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" data-mobilecollapse=\"true\" 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-\">\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-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" style=\"color: #000000; \">Part 1. Gibbs point process<\/h2>\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-math-plus\"><\/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-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\">\n\n<ol class=\"wp-block-list\">\n<li>Shearer&#8217;s bound on independent number of triangle-free graphs, uniform sampling \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall1-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Hard-core distribution, partition function, occupancy fraction, spacial Markov property \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall2-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Independent number of triangle-free graphs, sampling with hard-core distribution \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall3-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Sphere packing density, hard-sphere model \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall4-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Improved bound on expected sphere packing density \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall5-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Improved bound on expected sphere packing density 2 \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall6-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Maximise occupancy fraction and number of independent sets among regular graphs \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall7-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-1-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" style=\"color: #000000; \">Part 2. Polynomial methods<\/h2>\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-math-plus\"><\/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-1-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\">\n\n<ol start=\"8\" class=\"wp-block-list\">\n<li>Schwartz-Zippel lemma, polynomial identity testing and perfect matching testing \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall8-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Discrete Kakeya set is dense, Dvir&#8217;s proof and Bukh-Chao&#8217;s tight bound \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall9-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Joints theorem \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall10-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Capset problem and slice rank of hypermatrices \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall11-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Capset is exponentially small, Erd\u0151s-Szemer\u00e9di sunflower conjecture \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall12-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Combinatorial Nullstellensatz, Cauchy-Davenport \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall13-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Covering hypercube with affine hyperplanes, Chevalley-Warning, finding regular subgraphs, permanent lemma, Erd\u0151s-Ginzburg-Ziv \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall14-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-2-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" style=\"color: #000000; \">Part 3. Pseudorandomness<\/h2>\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-math-plus\"><\/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-2-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\">\n\n<ol start=\"15\" class=\"wp-block-list\">\n<li>Quasirandom graphs, induced subgraph counts, subgraph counts, 4-cycle counts, spectral gap, discrepancy, codegree \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall15-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Codegree implies induced subgraph counts \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall16-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Expander mixing lemma, discrepancy implies codegree \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall17-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Caylay graphs and their eigenvalues, characters of abelian groups, convolutions of two functions \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall18-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Equivalence of discrepancy and spectral gap for Caylay graphs \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall19-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Quasirandom sets in cyclic group, quasirandom 3-uniform hypergraph, quadratic uniformity \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall20-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-3-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" style=\"color: #000000; \">Part 4. Spectral methods<\/h2>\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-math-plus\"><\/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-3-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\">\n\n<ol start=\"21\" class=\"wp-block-list\">\n<li>Spectral theorem, Hoffman&#8217;s bound on indepdence number, Rayleigh quotient, Courant-Fischer \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall21-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Laplacian, Hoffman&#8217;s bound for irregular graphs, quadratic form defined by Laplacian and cuts of graphs \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall22-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Spectrum of normalised Laplacian, eigenvalues of Laplacian of complete graphs, stars and hypercubes \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall23-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Isoperimetric number, Cheeger constant, spectral gap defines expander \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall24-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Conductance, Fiedler&#8217;s algorithm, Trevisan&#8217;s proof of Cheeger&#8217;s inequality \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall25-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Robust Cheeger: bound conductance of a cut by Rayleigh quotient, Harper&#8217;s Isoperimetric inequality for hypercube, normalised Laplacian \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall26-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Perron-Frobenius, random walk, transition matrix, stationary distribution \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall27-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Spectrum of transition matrix, random walk on connected non-bipartite graph converges, mixing rate \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall28-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Total variation distance, mixing time and conductance, random walk on expanders mixes fast and resembles independent sampling \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall29-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-4-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\" style=\"color: #000000; \">Part 5. Concentration of measure<\/h2>\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-math-plus\"><\/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-4-ae90dfa2-aec9-4a7b-bee5-6d1fde4a03ab\">\n\n<ol start=\"30\" class=\"wp-block-list\">\n<li>Chernoff, Azuma-Hoeffding, McDiarmid&#8217;s inequality, deviation inequality for slice of Boolean cube \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall30-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><\/li>\n\n\n\n<li>Deviation inequality for slice of Hamming cube, application to sufficient conditions for small intersection of balls \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall31-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Exponential decay of intersection in Hamming space, application on improvement of Gilbert-Varshamov bound for q-ary codes \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall32-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Dimensionality reduction, Johnson-Lindenstrauss lemma \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall33-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><br><\/li>\n\n\n\n<li>Subspace embedding, least square regression \u00a0<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/fall34-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-0415eda5-3410-478b-86f1-c282e6ec35e0\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-6-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Summer 2021 Entropy method<\/h2>\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-6-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n<div style=\"gap: 20px;\" class=\"align-button-center ub-buttons orientation-button-row ub-flex-wrap wp-block-ub-button\" id=\"ub-button-94746f57-8ee0-4d0f-a65a-dc18e4a35022\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/entropy-SDU2021-summer.pdf\" target=\"_self\" 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; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-top-left-radius: 42px;; border-top-right-radius: 42px;; border-bottom-left-radius: 42px;; border-bottom-right-radius: 42px;; \">\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\">Note<\/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\/BV11f4y157f1\" target=\"_self\" 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: 52px;; border-top-right-radius: 52px;; border-bottom-left-radius: 52px;; border-bottom-right-radius: 52px;; \">\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\">Videos<\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>\n\n\n<ol class=\"wp-block-list\">\n<li>Definition of entropy, entropy axioms \u00e0 la Shannon-Khinchin, independence, non-negativity, monotonicity. <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/entropy1-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><\/li>\n\n\n\n<li>Chain rule, subadditivity, Shearer&#8217;s lemma, Loomis-Whitney inequality, entropy function satisfies axioms. <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/entropy2-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><\/li>\n\n\n\n<li>Summary of basic properties, volume of Hamming balls, triangle maximisation, triangle-intersecting family, entropy of uniform distribution. <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/10\/entropy3-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><\/li>\n\n\n\n<li>Axioms determine entropy function uniquely, Br\u00e9gman&#8217;s theorem on permanent of 0,1-matrices, Sidorenko&#8217;s conjecture for star of size 2. <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/entropy4-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><\/li>\n\n\n\n<li>Sidorenko&#8217;s conjecture for bipartite graphs with a dominating vertex, H-colourings. <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/entropy5-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><\/li>\n\n\n\n<li>Independent sets in bipartite regular graphs, counting matroids. <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2024\/10\/entropy6-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><\/li>\n\n\n\n<li>Tao&#8217;s entropy proof for sunflower. <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/entropy7-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a><\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-65b32e17-71a4-4154-b537-c2252824c4ea\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-7-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Spring 2021 Topics 1<\/h2>\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-7-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n<div style=\"gap: 20px;\" class=\"align-button-center ub-buttons orientation-button-row ub-flex-wrap wp-block-ub-button\" id=\"ub-button-a1303fa2-d811-4a2b-83ca-1a30a1e8b043\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.bilibili.com\/video\/BV11N41197P8\" target=\"_self\" 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-radius: 50px; \">\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\">Videos<\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle wp-block-ub-content-toggle-block\" id=\"ub-content-toggle-block-d5b6850b-451b-47e3-8fd8-9c553f411976\" data-mobilecollapse=\"true\" 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-\">\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-d5b6850b-451b-47e3-8fd8-9c553f411976\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d5b6850b-451b-47e3-8fd8-9c553f411976\" style=\"color: #000000; \">Part 1. Tur\u00e1n problem<\/h2>\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-math-plus\"><\/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-d5b6850b-451b-47e3-8fd8-9c553f411976\">\n\n<ol class=\"wp-block-list\">\n<li>Mantel, Tur\u00e1n thm, Erd\u0151s-Simonovits stability, Symmetrisation \u00e0 la Motzkin-Straus <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture1-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture1.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-1<\/mark><\/a><\/li>\n\n\n\n<li>Erd\u0151s-Simonovits-Stone, stability method, C_4-free graphs and Sidon set, K\u00f6vari-S\u00f3s-Tur\u00e1n <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture2-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture2.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-2<\/mark><\/a><br>-HW1: Exer 1.4, 2.3, 2.4 in Note 1; Exer 3.4 in Note 2; Prob 1, 2, 4 in Alon-Spencer (AS) Ch1.<\/li>\n\n\n\n<li>Even cycles from BFS, supersaturation, regularisation, cube, degeneracy <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture3-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture3.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-3<\/mark><\/a><\/li>\n\n\n\n<li>Random algebraic constructions, rational Tur\u00e1n exponent conjecture <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture4-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture4.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-4<\/mark><\/a><br>-HW2: Exer 1.8 in Note 3; Exer 3.5 in Note 4; Prob 1, 2, 5, 9 in (AS) Ch2.<\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-1-d5b6850b-451b-47e3-8fd8-9c553f411976\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d5b6850b-451b-47e3-8fd8-9c553f411976\" style=\"color: #000000; \">Part 2. Szemer\u00e9di regularity lemma<\/h2>\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-math-plus\"><\/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-1-d5b6850b-451b-47e3-8fd8-9c553f411976\">\n\n<ol start=\"5\" class=\"wp-block-list\">\n<li>Regularity lemma setup <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture5-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture5.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-5<\/mark><\/a><a href=\"http:\/\/homepages.warwick.ac.uk\/staff\/H.Liu.9\/topic-comb-lecture5.pdf\"><\/a><\/li>\n\n\n\n<li>Reduced graph, embedding lemma, counting lemma, triangle removal lemma <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture6-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture6.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-6<\/mark><\/a><br>-HW3: Exer 2.8 in Note 5; Exer 1.3, 3.3 in Note 6; Prob 1, 2, 3, 4 in (AS) Ch3.<\/li>\n\n\n\n<li>(6,3)-thm, Roth&#8217;s thm, induced matchings, Ramsey-Tur\u00e1n for K_4 <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture7-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture7.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-7<\/mark><\/a><a href=\"http:\/\/homepages.warwick.ac.uk\/staff\/H.Liu.9\/topic-comb-lecture7.pdf\"><\/a><\/li>\n\n\n\n<li>Linear Ramsey number for bounded degree graphs, spectral proof of the regularity lemma <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture8-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture8.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-8<\/mark><\/a><br>-HW4: Exer 3.3 in Note 7; Prob 1, 2, 4, 5 in (AS) Ch4.<\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-2-d5b6850b-451b-47e3-8fd8-9c553f411976\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d5b6850b-451b-47e3-8fd8-9c553f411976\" style=\"color: #000000; \">Part 3. Extremal set theory<\/h2>\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-math-plus\"><\/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-2-d5b6850b-451b-47e3-8fd8-9c553f411976\">\n\n<ol start=\"9\" class=\"wp-block-list\">\n<li>Sperner&#8217;s thm, LYM, (skewed) Bollob\u00e1s set-pairs inequalities, applications to Littlewood-Offord, saturation number <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture9-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture9.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-9<\/mark><\/a><a href=\"http:\/\/homepages.warwick.ac.uk\/staff\/H.Liu.9\/topic-comb-lecture9.pdf\"><\/a><\/li>\n\n\n\n<li>Erd\u0151s-Ko-Rado, applications of (skewed) set-pairs inequalities to counting maximal uniform intersecting families and fractional Helly <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture10-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture10.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-10<\/mark><\/a><br>\u00a0 \u00a0 HW5: Exer 3.3 in Note 9; Exer 1.2, 1.5 in Note 10; Prob 1, 2, 3 in (AS) Ch5.<\/li>\n\n\n\n<li>Fractional Helly, Kruskal-Katona, shift\/compression <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture11-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture11.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-11<\/mark><\/a><\/li>\n\n\n\n<li>Dimension argument, odd town even town, sets with two distinct distance, Frankl-Wilson on sets with restricted intersection, sets of unit vectors with no orthogonal pairs, Kahn-Kalai&#8217;s disproof of Borsuk&#8217;s conjecture <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture12-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture12.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-12<\/mark><\/a><br>-HW6: Fact 2.6 in Note 11; Prob 1, 2, 3 in (AS) Ch6.<\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-3-d5b6850b-451b-47e3-8fd8-9c553f411976\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d5b6850b-451b-47e3-8fd8-9c553f411976\" style=\"color: #000000; \">Part 4. Geometric constructions<\/h2>\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-math-plus\"><\/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-3-d5b6850b-451b-47e3-8fd8-9c553f411976\">\n\n<ol start=\"13\" class=\"wp-block-list\">\n<li>Behrend&#8217;s 3-AP-free\/Green&#8217;s corner-free construction, Erd\u0151s-Rothschild problem on books <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture13-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture13.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-13<\/mark><\/a><a href=\"http:\/\/homepages.warwick.ac.uk\/staff\/H.Liu.9\/topic-comb-lecture13.pdf\"><\/a><\/li>\n\n\n\n<li>Complex Bollob\u00e1s-Erd\u0151s graphs <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture14-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture14.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-14<\/mark><\/a><br>-HW7: Prob 1, 2, 3 in (AS) Ch7.<\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-4-d5b6850b-451b-47e3-8fd8-9c553f411976\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-d5b6850b-451b-47e3-8fd8-9c553f411976\" style=\"color: #000000; \">Part 5. Container theorem<\/h2>\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-math-plus\"><\/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-4-d5b6850b-451b-47e3-8fd8-9c553f411976\">\n\n<ol start=\"15\" class=\"wp-block-list\">\n<li>Kleitman-Winston graph container theorem, application to counting intersecting families <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture15-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture15.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-15<\/mark><\/a><a href=\"http:\/\/homepages.warwick.ac.uk\/staff\/H.Liu.9\/topic-comb-lecture15.pdf\"><\/a><\/li>\n\n\n\n<li>Hypergraph container, count maximal triangle-free graphs <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/lecture16-tab.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Tablet note<\/mark><\/a>  <a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/topic-comb-lecture16.pdf\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">Note-16<\/mark><\/a><\/li>\n<\/ol>\n\n<\/div>\n\t\t<\/div>\n<\/div>\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-6e00a885-d7c4-46e3-8404-49a165e869cb\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-8-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Robust sublinear expander<\/h2>\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-8-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n<div style=\"gap: 20px;\" class=\"align-button-center ub-buttons orientation-button-row ub-flex-wrap wp-block-ub-button\" id=\"ub-button-5ef1c524-4158-4d9c-9b22-8836d2995016\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/sublinear-expander-note-July16.pdf\" target=\"_self\" 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; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-radius: 44px; \">\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\">Note<\/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\/BV1tA411v7pz?p=1\" target=\"_self\" 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-radius: 55px; \">\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\">Videos<\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>\n<\/div>\n\t\t<\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\" style=\"border-color: #f1f1f1; \" id=\"ub-content-toggle-panel-block-1fb8eec0-6af9-4982-bcbe-7a435438c6c1\">\n\t\t\t<div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color: #f1f1f1;\" aria-controls=\"ub-content-toggle-panel-9-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" tabindex=\"0\">\n\t\t\t<h2 class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b754e0a3-78af-4ce8-86e3-85c26b5d882c\" style=\"color: #000000; \">Cycles and trees in (pseudorandom)graphs<\/h2>\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-9-b754e0a3-78af-4ce8-86e3-85c26b5d882c\">\n<div style=\"gap: 20px;\" class=\"align-button-center ub-buttons orientation-button-row ub-flex-wrap wp-block-ub-button\" id=\"ub-button-b8e5981f-21a2-4604-aeeb-25cb5af1a15e\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/03\/cycles-trees-Oct17.pdf\" target=\"_self\" 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; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-radius: 56px; \">\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\">Note<\/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=fF3ize-IOHA&amp;list=PLu06QHBZ8gatzn4k7fBqqCy5r2iAZJFCi&amp;ab_channel=JaehoonKim\" target=\"_self\" 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-radius: 49px; \">\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\">Videos<\/span>\n\t\t\t\t<\/div>\n\t\t\t<\/a>\n\t\t<\/div><\/div>\n<\/div>\n\t\t<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":5,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-98","page","type-page","status-publish","hentry"],"featured_image_src":null,"_links":{"self":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/pages\/98","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/comments?post=98"}],"version-history":[{"count":56,"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/pages\/98\/revisions"}],"predecessor-version":[{"id":495,"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/pages\/98\/revisions\/495"}],"wp:attachment":[{"href":"https:\/\/www.ibs.re.kr\/ecopro\/hongliu\/wp-json\/wp\/v2\/media?parent=98"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}