{"id":188168,"date":"2012-07-24T00:00:00","date_gmt":"2012-07-30T19:40:36","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/summer-number-theory-day-session-2\/"},"modified":"2016-08-22T11:26:44","modified_gmt":"2016-08-22T18:26:44","slug":"summer-number-theory-day-session-2","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/summer-number-theory-day-session-2\/","title":{"rendered":"Summer Number Theory Day; Session 2"},"content":{"rendered":"<div class=\"asset-content\">\n<p>SPEAKER:  Kiran Kedlaya<br \/>\nTITLE:  The Robbins phenomenon: unexpected numerical stability in p-adic arithmetic<\/p>\n<p>ABSTRACT:<br \/>\nSince one cannot represent an arbitrary real number on a computer, it is standard to approximate real-number arithmetic using floating-point approximations. The situation is similar for p-adic numbers; we begin by introducing the analogue of floating-point arithmetic for p-adics. We then describe some known and conjectural examples of p-adic numerical stability in which algebraic structures (e.g., cluster algebras) work behind the scenes to keep the loss of numerical precision much lower than one might initially expect. A key example is the Dodgson (Lewis Carroll) condensation algorithm for computing determinants, for which we obtain a partial result towards a conjecture of Robbins. Joint work with Joe Buhler (CCR La Jolla).<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>SPEAKER: Kiran Kedlaya TITLE: The Robbins phenomenon: unexpected numerical stability in p-adic arithmetic ABSTRACT: Since one cannot represent an arbitrary real number on a computer, it is standard to approximate real-number arithmetic using floating-point approximations. The situation is similar for p-adic numbers; we begin by introducing the analogue of floating-point arithmetic for p-adics. We then [&hellip;]<\/p>\n","protected":false},"featured_media":197039,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-188168","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/JVs7Aq4QTkg","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/188168","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/188168\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/197039"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=188168"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=188168"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=188168"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=188168"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=188168"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=188168"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=188168"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=188168"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=188168"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=188168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}