{"id":533,"date":"2018-09-11T14:37:38","date_gmt":"2018-09-11T21:37:38","guid":{"rendered":"https:\/\/colleges.claremont.edu\/ccms\/?post_type=tribe_events&#038;p=533"},"modified":"2018-09-26T08:16:43","modified_gmt":"2018-09-26T15:16:43","slug":"talk-by-edray-goins-pomona-college","status":"publish","type":"tribe_events","link":"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/","title":{"rendered":"An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College)"},"content":{"rendered":"<p>In 1846, Ernst Eduard Kummer conjectured a distribution of values of a cubic Gauss sum after computing a few values by hand.\u00a0 This was forgotten about for nearly 100 years until John von Neumann and Herman Goldstine attempted to verify the conjecture as a way to test the new ENIAC machine in 1953.\u00a0 They found evidence that the conjecture was false, but trusted Kummer more than they did their digital computer.\u00a0 The conjecture would hold until 1979, when Roger Heath-Brown and Samuel Patterson proved it to be false.<\/p>\n<p>A few years earlier in 1965, Mikio Sato and John Tate independently came up with a conjecture which gave the correct distribution of these cubic Gauss sums &#8212; although it was expressed slightly differently in terms of counting points of elliptic curves over finite fields.\u00a0 In this talk, we give an overview of the Sato-Tate Conjecture, present an approach by Jean-Pierre Serre following his paper from 1967, then sketch the 2006 proof of the conjecture following the ideas of Laurent Clozel, Michael Harris, Nicholas Shepherd-Barron and Richard Taylor.<\/p>\n<p>Here are the slides of this lecture:\u00a0<a href=\"https:\/\/colleges.claremont.edu\/ccms\/wp-content\/uploads\/sites\/19\/2018\/09\/antcs.pdf\">Edray Goins&#8217; slides<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In 1846, Ernst Eduard Kummer conjectured a distribution of values of a cubic Gauss sum after computing a few values by hand.\u00a0 This was forgotten about for nearly 100 years [&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-533","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>An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College) - 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\/talk-by-edray-goins-pomona-college\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College) - Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"og:description\" content=\"In 1846, Ernst Eduard Kummer conjectured a distribution of values of a cubic Gauss sum after computing a few values by hand.\u00a0 This was forgotten about for nearly 100 years [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/\" \/>\n<meta property=\"og:site_name\" content=\"Claremont Center for the Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2018-09-26T15:16:43+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/\",\"name\":\"An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College) - Claremont Center for the Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\"},\"datePublished\":\"2018-09-11T21:37:38+00:00\",\"dateModified\":\"2018-09-26T15:16:43+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/#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\":\"An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/colleges.claremont.edu\/ccms\/#website\",\"url\":\"https:\/\/colleges.claremont.edu\/ccms\/\",\"name\":\"Claremont Center for the Mathematical Sciences\",\"description\":\"Proudly Serving the Math Community at the Claremont Colleges Since 2007\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/colleges.claremont.edu\/ccms\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College) - Claremont Center for the Mathematical Sciences","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/","og_locale":"en_US","og_type":"article","og_title":"An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College) - Claremont Center for the Mathematical Sciences","og_description":"In 1846, Ernst Eduard Kummer conjectured a distribution of values of a cubic Gauss sum after computing a few values by hand.\u00a0 This was forgotten about for nearly 100 years [&hellip;]","og_url":"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/","og_site_name":"Claremont Center for the Mathematical Sciences","article_modified_time":"2018-09-26T15:16:43+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/","url":"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/","name":"An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College) - Claremont Center for the Mathematical Sciences","isPartOf":{"@id":"https:\/\/colleges.claremont.edu\/ccms\/#website"},"datePublished":"2018-09-11T21:37:38+00:00","dateModified":"2018-09-26T15:16:43+00:00","breadcrumb":{"@id":"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/colleges.claremont.edu\/ccms\/event\/talk-by-edray-goins-pomona-college\/#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":"An Introduction to the Sato-Tate Conjecture (Edray Goins, Pomona College)"}]},{"@type":"WebSite","@id":"https:\/\/colleges.claremont.edu\/ccms\/#website","url":"https:\/\/colleges.claremont.edu\/ccms\/","name":"Claremont Center for the Mathematical Sciences","description":"Proudly Serving the Math Community at the Claremont Colleges Since 2007","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/colleges.claremont.edu\/ccms\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"ticketed":false,"_links":{"self":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events\/533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events"}],"about":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/types\/tribe_events"}],"author":[{"embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/users\/73"}],"version-history":[{"count":0,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events\/533\/revisions"}],"wp:attachment":[{"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/media?parent=533"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tags?post=533"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/colleges.claremont.edu\/ccms\/wp-json\/wp\/v2\/tribe_events_cat?post=533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}