{"id":1139,"date":"2021-05-15T13:07:39","date_gmt":"2021-05-15T17:07:39","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/rcrew\/?page_id=1139"},"modified":"2026-03-19T08:16:55","modified_gmt":"2026-03-19T12:16:55","slug":"homological-algebra-seminar","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/rcrew\/homological-algebra-seminar\/","title":{"rendered":"Homological Algebra Seminar"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Homological Algebra Seminar<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Description<\/h3>\n\n\n\n<p>The seminar will run every Wednesday from 10am to 11am during Summer C, via Zoom. We will cover the following topics:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Abelian Categories<\/li>\n<li>Derived Functors<\/li>\n<li>Ext and Tor functors<\/li>\n<li>Sheaf cohomology<\/li>\n<li>Spectral Sequences<\/li><\/ul>\n\n\n\n<p>It time permits I may cover some additional topics, such as group cohomology, Hochschild cohomology, or derived categories.<\/p>\n\n\n\n\n\n<h3 class=\"wp-block-heading\">General references<\/h3>\n\n\n\n<p>The first three of these can be found on the internet in PDF form:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Hilton and Stammbach, <em>A Course in Homological Algebra<\/em>. A good basic treatment but mostly focuses on module categories.<\/li>\n<li>Weibel, <em>An Introduction to Homological Algebra<\/em>. In spite of the title, a more advanced treatment than Hilton-Stammbach. I will be using this a lot.<\/li>\n<li>Grothendieck, <em>Sur quelque points d&#8217;algebre homologique<\/em>, Tohoku J. Math <strong>9<\/strong> no. 2, 1957. This is the classic reference, and the fact that it&#8217;s in French will be the least of your worries. The wikipedia page has a pointer to an English translation.<\/li>\n<li>Gelfand and Manin, <em>Methods of Homological Algebra<\/em>. Lots of interesting stuff but very idiosyncratic.<\/li>\n<li>Chapter 12 of the <a href=\"https:\/\/stacks.math.columbia.edu\/\">Stacks Project<\/a> is devoted to homological algebra in the setting of abelian categories.<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Lectures<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 1<\/a> &#8211; Additive Categories<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 2<\/a> &#8211; Abelian Categories<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 3<\/a> &#8211; Exactness in Abelian Categories<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 4<\/a> &#8211; Projective and Injective objects<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 5<\/a> &#8211; Exactness, Complexes, Homology<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 6<\/a> &#8211; Additive Functors, Resolutions, Homotopies<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 7<\/a> &#8211; Derived Functors<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 8<\/a> &#8211; Universal properties of derived functors. Ext groups<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture <\/a>9 &#8211; Interpretation of the Ext groups. Tor functors<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 10<\/a> (7\/21\/21) &#8211; Sheaves on a topological space<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 11<\/a> (7\/23\/21) &#8211; Properties of abelian sheaves. Direct images, local and global Ext<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 12<\/a> &#8211; Spectral Sequences<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 13<\/a> &#8211; The Spectral Sequence of a Composite Functor. Applications.<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/rcrew\/content-removed\/\">Lecture 14<\/a> &#8211; Derived Categories (introduction)<\/li>\n<li>Lecture 15 &#8211; Triangulated Categories<\/li><\/ul>\n\n\n\n<p>Lectures 14 and 15 will not actually be delivered but are posted here for your, ahem entertainment. Enjoy!<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":313,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1139","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/rcrew\/wp-json\/wp\/v2\/pages\/1139","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/rcrew\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/rcrew\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/rcrew\/wp-json\/wp\/v2\/users\/313"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/rcrew\/wp-json\/wp\/v2\/comments?post=1139"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/rcrew\/wp-json\/wp\/v2\/pages\/1139\/revisions"}],"predecessor-version":[{"id":1312,"href":"https:\/\/people.clas.ufl.edu\/rcrew\/wp-json\/wp\/v2\/pages\/1139\/revisions\/1312"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/rcrew\/wp-json\/wp\/v2\/media?parent=1139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}