{"id":2556,"date":"2022-01-24T22:20:30","date_gmt":"2022-01-25T06:20:30","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=2556"},"modified":"2022-03-25T22:20:25","modified_gmt":"2022-03-26T05:20:25","slug":"antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/","title":{"rendered":"Covering by polynomial planks (Alexey Glazyrin, University of Texas Rio Grande Valley)"},"content":{"rendered":"

In 1932, Tarski conjectured that a convex body of width 1 can be covered by planks, regions between two parallel hyperplanes, only if the total width of planks is at least 1. In 1951, Bang proved the conjecture of Tarski. In this work we study the polynomial version of Tarski’s plank problem.<\/p>\n

We note that the recent polynomial proofs of the spherical and complex plank covering problems by Zhao and Ortega-Moreno give some general information on zeros of real and complex polynomials restricted to the unit sphere. As a corollary of these results, we establish several generalizations of the Bang plank covering theorem.
\n
Using the polynomial approach, we also prove the strengthening of the Fejes T\u00f3th zone conjecture on covering a sphere by spherical segments, closed parts of the sphere between two parallel hyperplanes. In particular, we show that the sum of angular widths of spherical segments covering the whole sphere is at least\u00a0\u03c0.<\/p>\n

This is a joint work with Roman Karasev and Alexandr Polyanskii.<\/p>\n","protected":false},"excerpt":{"rendered":"

In 1932, Tarski conjectured that a convex body of width 1 can be covered by planks, regions between two parallel hyperplanes, only if the total width of planks is at […]<\/p>\n","protected":false},"author":73,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_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,"_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":"","_tec_slr_enabled":"","_tec_slr_layout":""},"tags":[],"tribe_events_cat":[13],"class_list":["post-2556","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-antc-seminar","cat_antc-seminar"],"acf":[],"yoast_head":"\nCovering by polynomial planks (Alexey Glazyrin, University of Texas 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\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Covering by polynomial planks (Alexey Glazyrin, University of Texas Rio Grande Valley) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"In 1932, Tarski conjectured that a convex body of width 1 can be covered by planks, regions between two parallel hyperplanes, only if the total width of planks is at […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-26T05:20:25+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/\",\"name\":\"Covering by polynomial planks (Alexey Glazyrin, University of Texas Rio Grande Valley) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2022-01-25T06:20:30+00:00\",\"dateModified\":\"2022-03-26T05:20:25+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/#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\":\"ANTC seminar — Alexey Glazyrin (University of Texas 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":"Covering by polynomial planks (Alexey Glazyrin, University of Texas 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\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/","og_locale":"en_US","og_type":"article","og_title":"Covering by polynomial planks (Alexey Glazyrin, University of Texas Rio Grande Valley) - Claremont Center for the Mathematical Sciences","og_description":"In 1932, Tarski conjectured that a convex body of width 1 can be covered by planks, regions between two parallel hyperplanes, only if the total width of planks is at […]","og_url":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/","og_site_name":"Claremont Center for the Mathematical Sciences","article_modified_time":"2022-03-26T05:20:25+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/","url":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/","name":"Covering by polynomial planks (Alexey Glazyrin, University of Texas Rio Grande Valley) - Claremont Center for the Mathematical Sciences","isPartOf":{"@id":"https:\/\/colleges.claremont.edu\/ccms\/#website"},"datePublished":"2022-01-25T06:20:30+00:00","dateModified":"2022-03-26T05:20:25+00:00","breadcrumb":{"@id":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley\/#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":"ANTC seminar — Alexey Glazyrin (University of Texas 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"}]}},"ticketed":false,"_links":{"self":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events\/2556","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events"}],"about":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/types\/tribe_events"}],"author":[{"embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/users\/73"}],"version-history":[{"count":0,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events\/2556\/revisions"}],"wp:attachment":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/media?parent=2556"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tags?post=2556"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events_cat?post=2556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}