{"id":3003,"date":"2022-11-28T08:31:57","date_gmt":"2022-11-28T16:31:57","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=3003"},"modified":"2022-11-28T08:31:57","modified_gmt":"2022-11-28T16:31:57","slug":"on-discrete-subgroups-of-euclidean-spaces-lenny-fukshansky-cmc","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/on-discrete-subgroups-of-euclidean-spaces-lenny-fukshansky-cmc\/","title":{"rendered":"On discrete subgroups of Euclidean spaces (Lenny Fukshansky, CMC)"},"content":{"rendered":"<p>Let x_1,&#8230;,x_n be an overdetermined spanning set for the Euclidean space R^k, where n &gt; k. Let L be the integer span of these vectors. Then L is an additive subgroup of R^n. When is it discrete in R^n? Naturally, this depends on the choice of the spanning set, but in which way? We will review some classical results leading up to this question and then will discuss some more recent developments.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let x_1,&#8230;,x_n be an overdetermined spanning set for the Euclidean space R^k, where n &gt; k. Let L be the integer span of these vectors. Then L is an additive [&hellip;]<\/p>\n","protected":false},"author":195,"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":[14],"class_list":["post-3003","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-analysis-seminar","cat_analysis-seminar"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>On discrete subgroups of Euclidean spaces (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\/?post_type=tribe_events&p=3003\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"On discrete subgroups of Euclidean spaces (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Let x_1,&#8230;,x_n be an overdetermined spanning set for the Euclidean space R^k, where n &gt; k. Let L be the integer span of these vectors. Then L is an additive [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&amp;p=3003\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\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\/?post_type=tribe_events&p=3003\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3003\",\"name\":\"On discrete subgroups of Euclidean spaces (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2022-11-28T16:31:57+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3003#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3003\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3003#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\":\"On discrete subgroups of Euclidean spaces (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":"On discrete subgroups of Euclidean spaces (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\/?post_type=tribe_events&p=3003","og_locale":"en_US","og_type":"article","og_title":"On discrete subgroups of Euclidean spaces (Lenny Fukshansky, CMC) - Claremont Center for the Mathematical Sciences","og_description":"Let x_1,&#8230;,x_n be an overdetermined spanning set for the Euclidean space R^k, where n &gt; k. 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