{"id":963,"date":"2018-12-05T09:10:33","date_gmt":"2018-12-05T17:10:33","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=963"},"modified":"2019-01-23T14:35:04","modified_gmt":"2019-01-23T22:35:04","slug":"antc-talk-lenny-fukshansky-cmc","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-lenny-fukshansky-cmc\/","title":{"rendered":"Lattices from group frames and vertex transitive graphs (Lenny Fukshansky, CMC)"},"content":{"rendered":"<p>Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. A particularly nice class of such frames is generated as orbits under irreducible actions of finite groups of orthogonal matrices: these are called irreducible group frames. Integer spans of rational irreducible group frames form Euclidean lattices with some very nice geometric properties, called strongly eutactic lattices. We discuss this construction, focusing on an especially interesting infinite family in arbitrarily large dimensions, which comes from vertex transitive graphs. We demonstrate several examples of such lattices from graphs that exhibit some rather fascinating properties. This is joint work with D. Needell, J. Park and J. Xin.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. A particularly nice class of such frames is generated as orbits under irreducible actions of finite groups [&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-963","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>Lattices from group frames and vertex transitive graphs (Lenny Fukshansky, CMC) - 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-talk-lenny-fukshansky-cmc\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lattices from group frames and vertex transitive graphs (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. A particularly nice class of such frames is generated as orbits under irreducible actions of finite groups [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-lenny-fukshansky-cmc\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2019-01-23T22:35:04+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-talk-lenny-fukshansky-cmc\/\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-lenny-fukshansky-cmc\/\",\"name\":\"Lattices from group frames and vertex transitive graphs (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2018-12-05T17:10:33+00:00\",\"dateModified\":\"2019-01-23T22:35:04+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-lenny-fukshansky-cmc\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-lenny-fukshansky-cmc\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-lenny-fukshansky-cmc\/#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\":\"Lattices from group frames and vertex transitive graphs (Lenny Fukshansky, CMC)\"}]},{\"@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":"Lattices from group frames and vertex transitive graphs (Lenny Fukshansky, CMC) - 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-talk-lenny-fukshansky-cmc\/","og_locale":"en_US","og_type":"article","og_title":"Lattices from group frames and vertex transitive graphs (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences","og_description":"Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. 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