{"id":258,"date":"2023-11-09T11:30:06","date_gmt":"2023-11-09T11:30:06","guid":{"rendered":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=258"},"modified":"2023-11-09T11:30:06","modified_gmt":"2023-11-09T11:30:06","slug":"perverse-sheaves-and-the-decomposition-theorem","status":"publish","type":"page","link":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=258","title":{"rendered":"Perverse sheaves and the decomposition theorem"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\" id=\"Working_Seminar_Winter_2016\">Working Seminar Winter&nbsp;2016<a href=\"https:\/\/hodge.maths.ed.ac.uk\/tiki\/PervSheaves#Working_Seminar_Winter_2016\"><\/a><\/h2>\n\n\n\n<p><br>The aim of this working seminar is to give an introduction to Intersection (Co)Homology, Perverse Sheaves, the Decomposition Theorem, and end up with a tour of some classical and modern applications and conjectures. We will try to develop as much as possible &#8220;ground up&#8221;, so no particular pre-knowledge is assumed.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"Schedule\">Schedule<a href=\"https:\/\/hodge.maths.ed.ac.uk\/tiki\/PervSheaves#Schedule\"><\/a><\/h2>\n\n\n\n<p><br>All talks taking place Tuesdays, 1-2pm, in JCMB 5326.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a><strong>Organisation and introduction (Martina Lanini)<\/strong><\/a><br>12th January 2016, 1:00pm to 2:00pm<\/li>\n\n\n\n<li><a><strong>Introduction to Intersection Homology (Johan Martens)<\/strong><\/a><br>19th January 2016, 1:00pm to 2:00pm<\/li>\n\n\n\n<li><a><strong>Sheaf cohomology (Tim Weelinck)<\/strong><\/a><br>26th January 2016, 1:00pm to 2:00pm<\/li>\n\n\n\n<li><a><strong>Introduction to Derived Categories &amp; the 6 functor formalism (Jenny August)<\/strong><\/a><br>2nd February 2016, 1:00pm to 2:00pm<\/li>\n\n\n\n<li><a><strong>t-structures &amp; perverse sheaves (Matt Booth)<\/strong><\/a><br>9th February 2016, 1:00pm to 2:00pm<\/li>\n\n\n\n<li><a><strong>More on t-structures &amp; perverse sheaves (Matt Booth)<\/strong><\/a><br>23rd February 2016, 1:00pm to 2:00pm<\/li>\n\n\n\n<li><a><strong>Deligne&#8217;s construction of Intersection Cohomology (Salvatore Dolce)<\/strong><\/a><br>1st March 2016, 1:00pm to 2:00pm<\/li>\n\n\n\n<li><a><strong>Decomposition Theorem &#8211; Statement + Examples (David Jordan)<\/strong><\/a><br>8th March 2016, 1:00pm to 2:00pm<\/li>\n\n\n\n<li><a><strong>Comments on the proof of the Decomposition Theorem using Hodge Theory<\/strong><\/a><br>15th March 2016, 1:00pm to 2:00pm<\/li>\n\n\n\n<li><a><strong>The P=W conjecture (Johan Martens)<\/strong><\/a><br>12th April 2016, 10:30am to 12:00pm JCMB 5327<\/li>\n<\/ul>\n\n\n\n<p><a href=\"https:\/\/calendar.google.com\/calendar\/embed?src=48o8ullief5kjdk4d6e8gk1v7g@group.calendar.google.com&amp;ctz=Europe\/London&amp;mode=AGENDA\">(Open in Google Calendar)<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"Main_references:\">Main references:<a href=\"https:\/\/hodge.maths.ed.ac.uk\/tiki\/PervSheaves#Main_references:\"><\/a><\/h2>\n\n\n\n<p><br>The literature on this topic is vast. The three main sources we will use for the bulk of the seminar are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>M.A. de Cataldo and L. Migliorini, The decomposition theorem, perverse sheaves and the topology of algebraic maps. Bull. Amer. Math. Soc. (N.S.) 46 (2009), no. 4, 535\u2013633. Available&nbsp;<a target=\"_blank\" href=\"http:\/\/www.ams.org\/leavingmsn?url=http:\/\/dx.doi.org\/10.1090\/S0273-0979-09-01260-9\" rel=\"noreferrer noopener\">online<\/a>.<\/li>\n\n\n\n<li>F. Kirwan and J. Woolf, An introduction to intersection homology theory. Second edition. Chapman &amp; Hall\/CRC, Boca Raton, FL, 2006.&nbsp;<a target=\"_blank\" href=\"http:\/\/www.ams.org\/leavingmsn?url=http:\/\/dx.doi.org\/10.1201\/b15885\" rel=\"noreferrer noopener\">Book website.<\/a><\/li>\n\n\n\n<li>Georgie Williamson, An illustrated guide to perverse sheaves, unpublished notes, available&nbsp;<a target=\"_blank\" href=\"http:\/\/people.mpim-bonn.mpg.de\/geordie\/perverse_course\/lectures.pdf\" rel=\"noreferrer noopener\">online<\/a>.<\/li>\n<\/ul>\n\n\n\n<p><br>Other useful references will be pointed out during the semester.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"Extra_material\">Extra material<a href=\"https:\/\/hodge.maths.ed.ac.uk\/tiki\/PervSheaves#Extra_material\"><\/a><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/hodge.maths.ed.ac.uk\/wp-content\/uploads\/2023\/11\/IntroTalkPerverseSheaves.pdf\" data-type=\"attachment\" data-id=\"259\">IntroTalkPerverseSheaves.pdf<\/a><\/li>\n<\/ul>\n\n\n\n<p>The seminar is coordinated by Martina Lanini and Johan Martens. All are welcome to attend. If you want to be included in the mailing list please email\u00a0<a class=\"\" href=\"mailto:johan.martens@ed.ac.uk\">johan.martens@ed.ac.uk<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Working Seminar Winter&nbsp;2016 The aim of this working seminar is to give an introduction to Intersection (Co)Homology, Perverse Sheaves, the Decomposition Theorem, and end up with a tour of some classical and modern applications and conjectures. We will try to develop as much as possible &#8220;ground up&#8221;, so no particular pre-knowledge is assumed. Schedule All [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":76,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-258","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/258","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=258"}],"version-history":[{"count":1,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/258\/revisions"}],"predecessor-version":[{"id":262,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/258\/revisions\/262"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/media\/76"}],"wp:attachment":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=258"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}