{"id":1372,"date":"2019-08-25T12:28:23","date_gmt":"2019-08-25T19:28:23","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=1372"},"modified":"2019-09-06T15:33:33","modified_gmt":"2019-09-06T22:33:33","slug":"topology-seminar-jesse-levitt-usc","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/topology-seminar-jesse-levitt-usc\/","title":{"rendered":"Topology Seminar: Jesse Levitt (USC)"},"content":{"rendered":"<div class=\"rps_bcd7\">\n<div dir=\"ltr\">\n<div id=\"x_divtagdefaultwrapper\" dir=\"ltr\">\n<p>Title: Understanding Structure\u00a0in the\u00a0Single Variable Knot Polynomials<\/p>\n<p>Abstract:<\/p>\n<p>We\u00a0examine the dimensionality and internal\u00a0structure of the aggregated data produced by the Alexander, Jones, and\u00a0Z<sub>0<\/sub>\u00a0polynomials using topological data analysis and dimensional reduction techniques. By examining several families of knots, including over 10 million distinct examples, we find that the Jones data is well described as a three dimensional manifold, the\u00a0Z<sub>0<\/sub>\u00a0data as a single two dimensional manifold and the Alexander data as a collection of two dimensional manifolds. We confirm each of these structural results using two independent &#8216;big data&#8217; techniques.\u00a0The ability to consider knots in this manner illuminates several interesting relationships that I hope to discuss at the conclusion of the talk. This collects joint work with\u00a0Mustafa Hajij and\u00a0Radmila Sazdanovic.<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Title: Understanding Structure\u00a0in the\u00a0Single Variable Knot Polynomials Abstract: We\u00a0examine the dimensionality and internal\u00a0structure of the aggregated data produced by the Alexander, Jones, and\u00a0Z0\u00a0polynomials using topological data analysis and dimensional reduction [&hellip;]<\/p>\n","protected":false},"author":105,"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":[17],"class_list":["post-1372","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-topology-seminar","cat_topology-seminar"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - 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