{"id":2787,"date":"2022-08-24T13:48:20","date_gmt":"2022-08-24T20:48:20","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=2787"},"modified":"2022-10-31T13:32:45","modified_gmt":"2022-10-31T20:32:45","slug":"antc-talk-arvind-suresh-university-of-arizona-tucson","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/antc-talk-arvind-suresh-university-of-arizona-tucson\/","title":{"rendered":"Factoring translates of polynomials (Arvind Suresh, University of Arizona &#8211; Tucson)"},"content":{"rendered":"<p>Given a degree d polynomial f(x) in Q[x], consider the subset S_f\u00a0 of Q consisting of rational numbers t for which the translated polynomial f(x) &#8211; t factors completely in Q[x]. For example, if f is linear or quadratic then S_f is always infinite, but if degree of f is at least 3, then interesting things can happen. In this talk, we discuss a connection between the set S_f and the classical Prouhet&#8211;Tarry&#8211;Escott problem (which asks for integer solutions to certain symmetric family of equations), and we present two infinite families of polynomials f for which S_f is infinite (upon replacing Q with certain number fields). Time permitting, we outline how these can then be used to produce algebraic curves over number fields having a record number of rational points (relative to their genus).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given a degree d polynomial f(x) in Q[x], consider the subset S_f\u00a0 of Q consisting of rational numbers t for which the translated polynomial f(x) &#8211; t factors completely in [&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-2787","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>Factoring translates of polynomials (Arvind Suresh, University of Arizona - Tucson) - 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=2787\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Factoring translates of polynomials (Arvind Suresh, University of Arizona - Tucson) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"Given a degree d polynomial f(x) in Q[x], consider the subset S_f\u00a0 of Q consisting of rational numbers t for which the translated polynomial f(x) &#8211; 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