{"id":1723,"date":"2020-05-10T15:15:21","date_gmt":"2020-05-10T12:15:21","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=1723"},"modified":"2020-07-21T22:08:15","modified_gmt":"2020-07-21T19:08:15","slug":"online-seminar-this-tuesday-at-1000-u-haifa-topology-geometry-seminar-on-may-12-2020","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=1723","title":{"rendered":"Online seminar, this Tuesday at 10:00, U. Haifa Topology &#038; Geometry seminar on May 12, 2020"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong><u>Geometry&nbsp;&amp; Topology Seminar<\/u><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Speaker:&nbsp;Drew Heard, (Regensburg University)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Topic:&nbsp;&nbsp;Rational local systems and connected finite loop spaces<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Place:&nbsp; This is an online seminar. Please email&nbsp;David Blanc &lt;<a href=\"mailto:blanc@math.haifa.ac.il\" target=\"_blank\" rel=\"noreferrer noopener\">blanc@math.haifa.ac.il<\/a>&gt; for the Zoom ID and password.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Time:&nbsp; &nbsp;10:00<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Date:&nbsp; Tuesday, May 12,&nbsp; 2020<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong><u>Abstract:<\/u><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group G has an algebraic model &#8211; that is, it is (Quillen) equivalent to the category of dg-modules over an abelian category. This conjecture has been verified in a number of cases. Of particular interest, are the full subcategories of free and cofree G-spectra, where the abelian categories are the derived category of dg-torsion and dg-L-complete H^*(BG)-modules respectively, at least when G is connected, as shown by Greenlees&#8211;Shipley (for free G-spectra) and Pol&#8211;Williamson (for cofree G-spectra). We take a different approach to these results, starting from the identification of cofree G-spectra as rational local systems on the classifying space of BG (equivalently, a rational spectrum parametizied over BG). We give an algebraic model for rational local systems over a connected finite loop space (X,BX), and show that when X = G we recover the (connected case of) results of Greenlees&#8211;Shipley and Pol&#8211;Williamson. Throughout, we pay careful attention to the role of torsion and complete objects in a stable category.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Geometry&nbsp;&amp; Topology Seminar Speaker:&nbsp;Drew Heard, (Regensburg University) Topic:&nbsp;&nbsp;Rational local systems and connected finite loop spaces Place:&nbsp; This is an online seminar. Please email&nbsp;David Blanc &lt;blanc@math.haifa.ac.il&gt; for the Zoom ID and password. Time:&nbsp; &nbsp;10:00 Date:&nbsp; Tuesday, May 12,&nbsp; 2020 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Abstract: Greenlees&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=1723\">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-1723","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\/1723","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=1723"}],"version-history":[{"count":2,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1723\/revisions"}],"predecessor-version":[{"id":1750,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1723\/revisions\/1750"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1723"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1723"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1723"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}