{"id":3297,"date":"2023-10-20T14:31:10","date_gmt":"2023-10-20T21:31:10","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3297"},"modified":"2023-10-20T14:31:57","modified_gmt":"2023-10-20T21:31:57","slug":"lonely-runners-and-my-favorite-polyhedron-matthias-beck-san-francisco-state-university","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/lonely-runners-and-my-favorite-polyhedron-matthias-beck-san-francisco-state-university\/","title":{"rendered":"Lonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University)"},"content":{"rendered":"

Title: <\/strong>Lonely Runners and My Favorite Polyhedron<\/p>\n

Speaker:<\/strong> Matthias Beck, Department of Mathematics, San Francisco State University<\/p>\n

Abstract: <\/strong>We study the\u00a0Lonely Runner Conjecture<\/i>, conceived by Wills in the 1960’s, and originally phrased in terms of Diophantine approximation: Given positive integers n_1, n_2, …, n_k, there exists a positive real number t such that for all 1 \u2264 j \u2264 k the distance of t n_j to the nearest integer is at least 1\/(k+1). This conjecture can be recast in lay terms: if k runners with different (constant) speeds move around a circular track of length 1, then for each runner there will be a time when they have distance at least 1\/k to the others. This (in)famous conjecture in combinatorial number theory is open for k \u2265 7.
We will give a brief history of the\u00a0Lonely Runner Conjecture\u00a0and some of its variants, emphasizing a view-obstruction approach by Cusick and recent work by Henze and Malikiosis; our goal is to promote a polyhedral\u00a0ansatz<\/i>\u00a0to the Lonely Runner Conjecture. Our results include affirmative instances that become (quite literally) visible through polyhedral geometry.<\/p>\n

Based on joint work with Serkan Hosten (SF State) and Matthias Schymura (Rostock).<\/p>\n

\n
\n
\n
\n
\n

Matthias Beck is a professor of mathematics at San Francisco State University and has had visiting positions at SUNY Binghamton, the Mathematical Sciences Research Institute in Berkeley, the Max-Planck-Institute in Bonn, Cornell University, Vassar College, and the Freie Universit\u00e4t in Berlin. Matt\u2019s research is in combinatorics and number theory, in particular, counting integer points in polyhedra and the application of these enumeration functions to various mathematical topics and problems. He (co-)authored four books and numerous research papers, many of which feature student coauthors. Matt was honored with the Mathematical Association of America’s Haimo Award for Distinguished College or University Teaching of Mathematics in 2013.x`<\/p>\n

\n
\n
\n
\n
<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Title: Lonely Runners and My Favorite Polyhedron Speaker: Matthias Beck, Department of Mathematics, San Francisco State University Abstract: We study the\u00a0Lonely Runner Conjecture, conceived by Wills in the 1960’s, and […]<\/p>\n","protected":false},"author":204,"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":[12],"class_list":["post-3297","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-colloquium","cat_colloquium"],"acf":[],"yoast_head":"\nLonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University) - 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\/?post_type=tribe_events&p=3297\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Title: Lonely Runners and My Favorite Polyhedron Speaker: Matthias Beck, Department of Mathematics, San Francisco State University Abstract: We study the\u00a0Lonely Runner Conjecture, conceived by Wills in the 1960’s, and […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3297\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-20T21:31:57+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=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3297\",\"url\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3297\",\"name\":\"Lonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/#website\"},\"datePublished\":\"2023-10-20T21:31:10+00:00\",\"dateModified\":\"2023-10-20T21:31:57+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3297#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3297\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/colleges.claremont.edu\\\/ccms\\\/?post_type=tribe_events&p=3297#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\":\"Lonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University)\"}]},{\"@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":"Lonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University) - 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\/?post_type=tribe_events&p=3297","og_locale":"en_US","og_type":"article","og_title":"Lonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University) - Claremont Center for the Mathematical Sciences","og_description":"Title: Lonely Runners and My Favorite Polyhedron Speaker: Matthias Beck, Department of Mathematics, San Francisco State University Abstract: We study the\u00a0Lonely Runner Conjecture, conceived by Wills in the 1960’s, and […]","og_url":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3297","og_site_name":"Claremont Center for the Mathematical Sciences","article_modified_time":"2023-10-20T21:31:57+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3297","url":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3297","name":"Lonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University) - Claremont Center for the Mathematical Sciences","isPartOf":{"@id":"https:\/\/colleges.claremont.edu\/ccms\/#website"},"datePublished":"2023-10-20T21:31:10+00:00","dateModified":"2023-10-20T21:31:57+00:00","breadcrumb":{"@id":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3297#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3297"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3297#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":"Lonely Runners and My Favorite Polyhedron (Matthias Beck, San Francisco State University)"}]},{"@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"}]}},"_links":{"self":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events\/3297","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\/204"}],"version-history":[{"count":0,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events\/3297\/revisions"}],"wp:attachment":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/media?parent=3297"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tags?post=3297"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events_cat?post=3297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}