{"id":441,"date":"2018-08-17T08:08:12","date_gmt":"2018-08-17T15:08:12","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=441"},"modified":"2018-11-16T14:54:28","modified_gmt":"2018-11-16T22:54:28","slug":"tba-2","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/tba-2\/","title":{"rendered":"Sperner&#8217;s lemma: generalizations and applications (Oleg Musin, UT Rio Grande Valley)"},"content":{"rendered":"<p>The classical Sperner &#8211;\u00a0 KKM (Knaster &#8211; Kuratowski &#8211; Mazurkiewicz) lemma has many applications\u00a0 in combinatorics, algorithms, game theory and mathematical economics. In this talk we consider generalizations of this lemma as well as Gale&#8217;s colored KKM lemma and Shapley&#8217;s KKMS theorem. It is shown that spaces and covers can be much more general and the boundary KKM rules can be substituted by more weaker boundary assumptions. These generalizations of Sperner&#8217;s lemma rely on homotopy invariants of covers\u00a0 that in fact are obstructions for extending a cover of a subspace A in X to a cover of\u00a0 X.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The classical Sperner &#8211;\u00a0 KKM (Knaster &#8211; Kuratowski &#8211; Mazurkiewicz) lemma has many applications\u00a0 in combinatorics, algorithms, game theory and mathematical economics. In this talk we consider generalizations of this [&hellip;]<\/p>\n","protected":false},"author":73,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":""},"tags":[],"tribe_events_cat":[13],"class_list":["post-441","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Sperner&#039;s lemma: generalizations and applications (Oleg Musin, UT Rio Grande Valley) - Claremont Center for the Mathematical Sciences<\/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:\/\/colleges.claremont.edu\/ccms\/event\/tba-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sperner&#039;s lemma: generalizations and applications (Oleg Musin, UT Rio Grande Valley) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"The classical Sperner &#8211;\u00a0 KKM (Knaster &#8211; Kuratowski &#8211; Mazurkiewicz) lemma has many applications\u00a0 in combinatorics, algorithms, game theory and mathematical economics. In this talk we consider generalizations of this [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/tba-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2018-11-16T22:54:28+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/tba-2\\\/\",\"url\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/tba-2\\\/\",\"name\":\"Sperner's lemma: generalizations and applications (Oleg Musin, UT Rio Grande Valley) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/#website\"},\"datePublished\":\"2018-08-17T15:08:12+00:00\",\"dateModified\":\"2018-11-16T22:54:28+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/tba-2\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/tba-2\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/event\\\/tba-2\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Events\",\"item\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/events\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Sperner&#8217;s lemma: generalizations and applications (Oleg Musin, UT Rio Grande Valley)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/#website\",\"url\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/\",\"name\":\"Claremont Center for the Mathematical Sciences\",\"description\":\"Proudly Serving the Math Community at the Claremont Colleges Since 2007\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Sperner's lemma: generalizations and applications (Oleg Musin, UT Rio Grande Valley) - Claremont Center for the Mathematical Sciences","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/colleges.claremont.edu\/ccms\/event\/tba-2\/","og_locale":"en_US","og_type":"article","og_title":"Sperner's lemma: generalizations and applications (Oleg Musin, UT Rio Grande Valley) - Claremont Center for the Mathematical Sciences","og_description":"The classical Sperner &#8211;\u00a0 KKM (Knaster &#8211; Kuratowski &#8211; Mazurkiewicz) lemma has many applications\u00a0 in combinatorics, algorithms, game theory and mathematical economics. 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