{"id":2398,"date":"2022-05-21T18:20:53","date_gmt":"2022-05-21T15:20:53","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2398"},"modified":"2022-05-29T13:09:30","modified_gmt":"2022-05-29T10:09:30","slug":"u-haifa-topology-geometry-seminar-sunday-may-22-2022-speaker-andrew-salch-wayne-state-title-stable-homotopy-groups-and-special-values-of-l-functions","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2398","title":{"rendered":"U. Haifa Topology &#038; Geometry seminar: Sunday, May 22, 2022. Speaker: Andrew Salch (Wayne State). Title: &#8220;Stable homotopy groups and special values of L-functions&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Time: <\/strong>17:00 (Israel Time)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Location: <\/strong>On Zoom<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recording:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/us02web.zoom.us\/rec\/share\/2p8IC8Cg-VEwNlgsDG_sQJRv-tPbLizEwXxI1DFuCzYujlmGkGa7ndhiUdxxLD9-.quz6ubBm7uCXOi-0\">https:\/\/us02web.zoom.us\/rec\/share\/2p8IC8Cg-VEwNlgsDG_sQJRv-tPbLizEwXxI1DFuCzYujlmGkGa7ndhiUdxxLD9-.quz6ubBm7uCXOi-0<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;In this talk, I will survey the known relationships between stable homotopy groups of Bousfield localizations of finite spectra and special values of L-functions. Given a p-local finite spectrum X, the &#8220;chromatic tower&#8221; of X is a tower of Bousfield localizations of X. The homotopy limit of this tower recovers X itself. A calculation of Ravenel and of Adams-Baird from the 1970s established that the homotopy groups of the first stage in this tower for the sphere spectrum, the E(1)-local sphere, are describable in terms of special values of the Riemann zeta-function. In the past 5 years, this theorem has been extended to a description, in terms of special values of L-functions arising in number theory, of the E(1)-local homotopy groups of many finite spectra other than the sphere spectrum. As a cute application, I give a topological proof of some cases of the Leopoldt conjecture, a well-known conjecture in algebraic number theory. Finally, time allowing, I explain what is known and what is conjectured about descriptions, in terms of special values of L-functions, of the orders of the homotopy groups of the higher layers in the chromatic tower (the E(n)-local layer for n&gt;1) of a finite spectrum.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>ZOOM COORDINATES:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/us02web.zoom.us\/j\/84987591026?pwd=aTJWcFlOSldKck5leGt2d25CYkRqZz09\">https:\/\/us02web.zoom.us\/j\/84987591026?pwd=aTJWcFlOSldKck5leGt2d25CYkRqZz09<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Meeting ID: 849 8759 1026<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Future speakers:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Markus Upmeier (Aberdeen) \u2013 May 29<sup>th<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Denis-Charles Cisinski (Regensburg) \u2013 June 5<sup>th<\/sup>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Time: 17:00 (Israel Time) Location: On Zoom Recording: https:\/\/us02web.zoom.us\/rec\/share\/2p8IC8Cg-VEwNlgsDG_sQJRv-tPbLizEwXxI1DFuCzYujlmGkGa7ndhiUdxxLD9-.quz6ubBm7uCXOi-0 Abstract. &nbsp;In this talk, I will survey the known relationships between stable homotopy groups of Bousfield localizations of finite spectra and special values of L-functions. Given a p-local finite spectrum X,&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2398\">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":[6,4],"tags":[],"class_list":["post-2398","post","type-post","status-publish","format-standard","hentry","category-gt-seminar","category-seminar"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2398","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=2398"}],"version-history":[{"count":3,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2398\/revisions"}],"predecessor-version":[{"id":2402,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2398\/revisions\/2402"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}