{"id":3055,"date":"2023-01-25T14:42:31","date_gmt":"2023-01-25T22:42:31","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=3055"},"modified":"2023-04-25T13:36:17","modified_gmt":"2023-04-25T20:36:17","slug":"antc-talk-christopher-perez-loyola-university-new-orleans","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-christopher-perez-loyola-university-new-orleans\/","title":{"rendered":"Towers and elementary embeddings in total relatively hyperbolic groups (Christopher Perez, Loyola University New Orleans)"},"content":{"rendered":"<p>In a remarkable series of papers Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers, and independently Olga Kharlampovich and Alexei Myasnikov did the same using equivalent structures they called regular NTQ groups. It was later proved by Chlo\u00e9 Perin that if H is an elementarily embedded subgroup (or elementary submodel) of a torsion-free hyperbolic group G, then G is a tower over H. We prove a generalization of Perin\u2019s result to toral relatively hyperbolic groups using JSJ and shortening techniques.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In a remarkable series of papers Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers, and independently Olga Kharlampovich and [&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-3055","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>Towers and elementary embeddings in total relatively hyperbolic groups (Christopher Perez, Loyola University New Orleans) - 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=3055\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Towers and elementary embeddings in total relatively hyperbolic groups (Christopher Perez, Loyola University New Orleans) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"In a remarkable series of papers Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers, and independently Olga Kharlampovich and [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&amp;p=3055\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2023-04-25T20:36:17+00:00\" \/>\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=3055\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3055\",\"name\":\"Towers and elementary embeddings in total relatively hyperbolic groups (Christopher Perez, Loyola University New Orleans) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2023-01-25T22:42:31+00:00\",\"dateModified\":\"2023-04-25T20:36:17+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3055#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3055\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&p=3055#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 talk &#8212; 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