{"id":513,"date":"2018-09-05T10:05:27","date_gmt":"2018-09-05T17:05:27","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=513"},"modified":"2018-09-26T10:43:10","modified_gmt":"2018-09-26T17:43:10","slug":"an-algebra-of-arcs-and-loops-on-a-surface","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/an-algebra-of-arcs-and-loops-on-a-surface\/","title":{"rendered":"An Algebra of Arcs and Knots on a Surface (Helen Wong, CMC)"},"content":{"rendered":"<p>The end of the previous century saw radical changes to three-dimensional topology, which arose from two completely different approaches. One breakthrough came from Bill Thurston&#8217;s introduction of hyperbolic geometry into the field. The second one came from the Vaughn Jones\u2019s discovery of a new &#8220;quantum&#8221; invariant for knots that brought in insight and techniques from mathematical physics and non-commutative algebra. It is widely believed that the two approaches are related.<\/p>\n<p>In this talk, we will focus on a point of connection introduced over five years ago by J. Roger and T. Yang.\u00a0 They defined an algebra of arcs and knots on a surface that is both\u00a0 obviously related to the quantum invariants\u00a0<i>and<\/i>\u00a0motivated by hyperbolic geometry.\u00a0 We will give a overview of what&#8217;s known about this algebra of arcs and knots on a surface.\u00a0 Warning: there will be lots of pictures of arcs and knots on surfaces.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The end of the previous century saw radical changes to three-dimensional topology, which arose from two completely different approaches. One breakthrough came from Bill Thurston&#8217;s introduction of hyperbolic geometry into [&hellip;]<\/p>\n","protected":false},"author":79,"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":[12],"class_list":["post-513","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-colloquium","cat_colloquium"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>An Algebra of Arcs and Knots on a Surface (Helen Wong, 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\/an-algebra-of-arcs-and-loops-on-a-surface\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An Algebra of Arcs and Knots on a Surface (Helen Wong, CMC) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"The end of the previous century saw radical changes to three-dimensional topology, which arose from two completely different approaches. 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