{"id":16896,"date":"2026-07-28T14:23:51","date_gmt":"2026-07-28T19:23:51","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=16896"},"modified":"2026-07-28T14:23:51","modified_gmt":"2026-07-28T19:23:51","slug":"ms-thesis-defense-ms-monica-cabria","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/ms-thesis-defense-ms-monica-cabria\/","title":{"rendered":"MS Thesis Defense: Ms. Monica Cabria"},"content":{"rendered":"

Convergences groups and Gromov Hyperbolic Spaces<\/h2>\n

Monica Cabria<\/strong>
\nGraduate Student<\/strong>
\nUniversity of Wisconsin-Milwaukee<\/strong><\/p>\n

This thesis investigates the relationship between convergence group actions and hyperbolic spaces. Since the 1990s, this relationship has been a significant theme in geometric group theory, revealing deep connections between geometry and dynamics. The goal of this thesis is to provide a streamlined introduction to these ideas and to clarify the proofs of several foundational results.<\/div>\n
<\/div>\n
In particular, we discuss a theorem of Tukia and Freden showing that properly discontinuous actions on hyperbolic spaces induce convergence group actions on their boundaries, and a theorem of Bowditch characterizing convergence group actions through the induced action on the space of distinct triples. Together, these results illustrate how geometric properties of hyperbolic spaces are reflected in the dynamics of group actions on their boundaries.<\/div>\n","protected":false},"excerpt":{"rendered":"

Convergences groups and Gromov Hyperbolic Spaces Monica Cabria Graduate Student University of Wisconsin-Milwaukee This thesis investigates the relationship between convergence group actions and hyperbolic spaces. Since the 1990s, this relationship has been a significant theme in geometric group theory, revealing …<\/p>\n","protected":false},"author":30596,"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":"","uwm_wg_additional_authors":[]},"tags":[],"tribe_events_cat":[64],"class_list":["post-16896","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-graduate-student-defenses","cat_graduate-student-defenses"],"uwm_unpublish_requested":false,"yoast_head":"\nMathematical 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:\/\/uwm.edu\/math\/event\/ms-thesis-defense-ms-monica-cabria\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MS Thesis Defense: Ms. Monica Cabria\" \/>\n<meta property=\"og:description\" content=\"Convergences groups and Gromov Hyperbolic Spaces Monica Cabria Graduate Student University of Wisconsin-Milwaukee This thesis investigates the relationship between convergence group actions and hyperbolic spaces. 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