{"id":949,"date":"2017-11-15T09:35:15","date_gmt":"2017-11-15T07:35:15","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=949"},"modified":"2017-11-23T11:51:37","modified_gmt":"2017-11-23T09:51:37","slug":"colloquium-monday-november-20-4-pm-speaker-shai-haran-technion-title-geometry-over-f1","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=949","title":{"rendered":"Colloquium: Monday, November 20, 4 pm. Speaker: Shai Haran (Technion). Title: &#8220;Geometry over F1&#8221;."},"content":{"rendered":"<p>We give two simple generalizations of commutative rings.<br \/>\nThey form (co)-complete categories, that contain commutative (semi-) rings (e.g.<br \/>\nf0; 1g \u2286 [0; 1] \u2286 [0; 1) with the usual multiplication x + y := maxfx; yg). But<br \/>\nthey also contains the &#8220;integers&#8221; ZR (and ZC), and the &#8220;residue fields&#8221; FR (and<br \/>\nFC), of the real (and complex) numbers. Here ZR is the collection of unit L2 balls,<br \/>\nand FR is the collection of spheres augmented with a 0. The initial object is &#8220;the<br \/>\nfield with one element&#8221; F1.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We give two simple generalizations of commutative rings. They form (co)-complete categories, that contain commutative (semi-) rings (e.g. f0; 1g \u2286 [0; 1] \u2286 [0; 1) with the usual multiplication x + y := maxfx; yg). But they also contains&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=949\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-949","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/949","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=949"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/949\/revisions"}],"predecessor-version":[{"id":950,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/949\/revisions\/950"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}