{"id":2631,"date":"2022-04-28T12:16:59","date_gmt":"2022-04-28T03:16:59","guid":{"rendered":"https:\/\/www.ibs.re.kr\/ecopro\/?page_id=2631"},"modified":"2022-09-20T15:51:53","modified_gmt":"2022-09-20T06:51:53","slug":"spring-2022","status":"publish","type":"page","link":"https:\/\/www.ibs.re.kr\/ecopro\/spring-2022\/","title":{"rendered":"Spring 2022"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Discrete Geometry<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>Time: every Tues and Thur 10:30-11:30am (KST), May 3 &#8211; July 14<\/li><li>Zoom: 890 901 6918, PW: 202204<\/li><\/ul>\n\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\"><li>No class on May 10.<\/li><li>Class on June 2 will be one hour earlier, i.e. 9:30-10:30am Korean time, due to conflict to our online seminar <a href=\"https:\/\/dimag.ibs.re.kr\/event\/2022-06-02\/\">https:\/\/dimag.ibs.re.kr\/event\/2022-06-02\/<\/a><\/li><li><span style=\"color: #000000;\" class=\"stk-highlight\">No class on June 28 and 30.<\/span><\/li><li><strong><span style=\"color: #cf2e2e;\" class=\"stk-highlight\">Classes on July 5, 7, 12 are moved to 16:00 KST.<\/span><\/strong><\/li><\/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-bcc6da4d-64a9-484e-9785-49402a984ba6\"><div class=\"ub-button-container\">\n\t\t\t<a href=\"https:\/\/www.overleaf.com\/read\/fbphghrwkpds\" 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; padding-top: 10px; padding-right: 10px; padding-bottom: 10px; padding-left: 10px; border-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\/BV1aS4y1h71b?spm_id_from=333.999.0.0\" 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-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<ol class=\"wp-block-list\"><li>5\/3: affine hull\/dependence, convex hull, cone, Separation thm, Farkas lem. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/05\/Disc-Geom1.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>5\/5: Carath\u00e9odory, Radon, Radon \u21d2 Helly. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/05\/Disc-Geom2.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>5\/12: Radon \u21d2 Carath\u00e9odory, colorful Carath\u00e9odory and application to directed cycle. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/05\/Disc-Geom3.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>5\/17: Polytope reduction trick, 2nd proof of Helly via sweeping argument. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/05\/Disc-Geom4.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>5\/19: Colorful Helly number could be larger than Helly number, multiple separation thm, 3rd proof of (colorful) Helly via Carath\u00e9odory and Farkas. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/05\/Disc-Geom5.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>5\/24: Infinite Helly requires compactness, applications of Helly: translate intersecting a family, half-spaces covering, Kirchberger&#8217;s thm. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/05\/Disc-Geom6.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>5\/26: Center point thm, Jung&#8217;s thm, Helly + Carath\u00e9odory \u21d2 weak Tverberg. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/05\/Disc-Geom7.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>5\/31: Tight example for Tverberg and Sarkaria&#8217;s proof. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/05\/Disc-Geom8.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>6\/2: Fractional Helly, 1st proof via Helly, 2nd proof via colorful Helly. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/06\/Disc-Geom9.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>6\/7: Boros-F\u00fcredi, point selection in 2-dim, tight example: stretched grid, staircase convexity. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/06\/Disc-Geom10.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>6\/9: Tverberg + Colorful Carath\u00e9odory or Fractional Helly \u21d2 First selection lemma, max covering number realised by random points. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/06\/Disc-Geom11.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>6\/14: Erd\u0151s-Simonovits supersaturation + Colorful Tverberg + Fractional Helly \u21d2 Second selection lemma. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/06\/Disc-Geom12.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>6\/16: Second selection + weak hypergraph regularity + Same type lemma \u21d2 Homogeneous selection lemma. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/06\/Disc-Geom13.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>6\/21: Order type, well-separated tuple, same type tranversal, Ham-Sandwich thm \u21d2 Same type lemma. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/06\/Disc-Geom14.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>6\/23: First selection lemma \u21d2 Weak \u025b-net theorem. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/06\/Disc-Geom15.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>7\/5: Better bound for planar case weak \u025b-net. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/Disc-Geom16.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>7\/7: Example of families with (p,q)-property, connection of (p,q)-thm to chi-boundedness. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/Disc-Geom17.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>7\/12: Fractional Helly + Weak \u025b-net + (p,q)-property retained (weakly) in blowups \u21d2 (p,q)-thm via doubling argument. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/Disc-Geom18.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><li>7\/14: (p,q)-thm via linear programming duality. <strong><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/Disc-Geom19.pdf\"><span style=\"color: #ff6900;\" class=\"stk-highlight\">Tablet note<\/span><\/a><\/strong><\/li><\/ol>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-stackable-image stk-block-image stk-block stk-f5375f8\" data-block-id=\"f5375f8\"><figure class=\"stk-img-wrapper stk-image--shape-stretch\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-2975\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/convexity-diagram.jpg\" width=\"1084\" height=\"707\" srcset=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/convexity-diagram.jpg 1084w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/convexity-diagram-300x196.jpg 300w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/convexity-diagram-1024x668.jpg 1024w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/convexity-diagram-768x501.jpg 768w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/07\/convexity-diagram-600x391.jpg 600w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-stackable-image stk-block-image stk-block stk-34dcda8\" data-block-id=\"34dcda8\"><figure class=\"stk-img-wrapper stk-image--shape-stretch\"><img loading=\"lazy\" decoding=\"async\" class=\"stk-img wp-image-2632\" src=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/04\/ECOPRO-online-course-2022-spring-scaled.jpeg\" width=\"1810\" height=\"2560\" srcset=\"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/04\/ECOPRO-online-course-2022-spring-scaled.jpeg 1810w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/04\/ECOPRO-online-course-2022-spring-212x300.jpeg 212w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/04\/ECOPRO-online-course-2022-spring-724x1024.jpeg 724w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/04\/ECOPRO-online-course-2022-spring-768x1086.jpeg 768w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/04\/ECOPRO-online-course-2022-spring-1086x1536.jpeg 1086w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/04\/ECOPRO-online-course-2022-spring-1448x2048.jpeg 1448w, https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/04\/ECOPRO-online-course-2022-spring-283x400.jpeg 283w\" sizes=\"auto, (max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Discrete Geometry Time: every Tues and Thur 10:30-11:30am (KST), May 3 &#8211; July 14 Zoom: 890 901 6918, PW: 202204 Announcement No class on May 10. Class on June 2 &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.ibs.re.kr\/ecopro\/spring-2022\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Spring 2022&#8221;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":2632,"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-2631","page","type-page","status-publish","has-post-thumbnail","hentry"],"featured_image_src":"https:\/\/www.ibs.re.kr\/ecopro\/wp-content\/uploads\/2022\/04\/ECOPRO-online-course-2022-spring-scaled.jpeg","yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Spring 2022 - 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-2022\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Spring 2022 - Extremal Combinatorics and Probability Group\" \/>\n<meta property=\"og:description\" content=\"Discrete Geometry Time: every Tues and Thur 10:30-11:30am (KST), May 3 &#8211; July 14 Zoom: 890 901 6918, PW: 202204 Announcement No class on May 10. 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