{"id":1355,"date":"2019-08-09T09:15:58","date_gmt":"2019-08-09T16:15:58","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=1355"},"modified":"2020-02-02T14:48:46","modified_gmt":"2020-02-02T22:48:46","slug":"antc-seminar-dmitriy-bilyk-university-of-minnesota","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-dmitriy-bilyk-university-of-minnesota\/","title":{"rendered":"Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota)"},"content":{"rendered":"<p>The talk will concentrate on open\u00a0<span class=\"x_gmail-il\">questions<\/span>\u00a0<span class=\"x_gmail-il\">related<\/span>\u00a0to the optimal\u00a0<span class=\"x_gmail-il\">bounds<\/span>\u00a0for the\u00a0<span class=\"x_gmail-il\">discrepancy<\/span>\u00a0of an $N$-point set in the $d$-dimensional unit cube. The so-called star-discrepancy measures the difference between the actual and expected number of points in axis-parallel rectangles, and thus measures the equidistribution of the set. This notion has been explored by H. Weyl, K. Roth, and many others, however many questions still remain open, especially in higher dimensions.\u00a0 We shall discuss the two main conjectures on the order of star-<span class=\"x_gmail-il\">discrepancy<\/span>\u00a0and present evidence in support of each one, as well as their connections to various areas of mathematics. In addition, we shall talk about\u00a0<span class=\"x_gmail-il\">discrepancy<\/span>\u00a0in other geometrical settings (rotated rectangles, balls, points on the sphere etc).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The talk will concentrate on open\u00a0questions\u00a0related\u00a0to the optimal\u00a0bounds\u00a0for the\u00a0discrepancy\u00a0of an $N$-point set in the $d$-dimensional unit cube. The so-called star-discrepancy measures the difference between the actual and expected number of [&hellip;]<\/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-1355","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 v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota) - 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-dmitriy-bilyk-university-of-minnesota\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"The talk will concentrate on open\u00a0questions\u00a0related\u00a0to the optimal\u00a0bounds\u00a0for the\u00a0discrepancy\u00a0of an $N$-point set in the $d$-dimensional unit cube. The so-called star-discrepancy measures the difference between the actual and expected number of [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-dmitriy-bilyk-university-of-minnesota\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2020-02-02T22:48:46+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-dmitriy-bilyk-university-of-minnesota\/\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-dmitriy-bilyk-university-of-minnesota\/\",\"name\":\"Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2019-08-09T16:15:58+00:00\",\"dateModified\":\"2020-02-02T22:48:46+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-dmitriy-bilyk-university-of-minnesota\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-dmitriy-bilyk-university-of-minnesota\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-seminar-dmitriy-bilyk-university-of-minnesota\/#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\":\"Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota)\"}]},{\"@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":"Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota) - 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-dmitriy-bilyk-university-of-minnesota\/","og_locale":"en_US","og_type":"article","og_title":"Discrepancy theory and related questions (Dmitriy Bilyk, University of Minnesota) - Claremont Center for the Mathematical Sciences","og_description":"The talk will concentrate on open\u00a0questions\u00a0related\u00a0to the optimal\u00a0bounds\u00a0for the\u00a0discrepancy\u00a0of an $N$-point set in the $d$-dimensional unit cube. 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