{"id":2027,"date":"2021-04-29T09:24:25","date_gmt":"2021-04-29T06:24:25","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2027"},"modified":"2021-09-12T13:08:38","modified_gmt":"2021-09-12T10:08:38","slug":"u-of-haifa-colloquium-4-5-21","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2027","title":{"rendered":"U. of Haifa Colloquium 4\/5\/21"},"content":{"rendered":"\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Speaker: Yakov Karasik (Technion)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-15e407c1-5ea5-4efc-aac7-4967c53b6da6\">Topic: Counting rational flags of $Z^n$<br><br>Place: This is an online seminar. Please email Yuval Ginosar \u201cginosar at math dot haifa dot ac dot il\u201d for the Zoom ID and password.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-89317a3d-c8f0-40a9-87ab-35fd9ef60741\">Date: Tuesday, May 4, 2021<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-066dd0bd-75d8-47ee-90e9-b0a8e3d6a345\">Time: 14:00<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-126383d7-2164-4ad9-b5d5-3857b7bc746a\"><strong>Abstract<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A subspace V of $ R^n$ is called rational (w.r.t. the lattice $Z^n$) if $ L=V \\cap&nbsp; Z^n$&nbsp; is a lattice of V which is, in turn, referred to as a primitive sub-lattice of $Z^n$&nbsp; . In 68 Schmidt, using rather basic number-theoretical tools, was able to provide an asymptotic expression (with an error term) for the number of d dimensional primitive lattices of covolume no bigger than T . A much more refined question is to perform this kind of counting in a subset obtained by restricting different parameters associated to them. For instance, one considers the direction, the shape, the homothety class of L or of its \u201ccomplement\u201d. 30 years later(!), Schmidt was able to obtain partial results w.r.t. this refinement but not enough to deduce equidistribution of all of the aforementioned parameters.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this talk, I will talk about a series of works together with T. Horesh where we use a dynamical approach to expand the results of Schmidt in two major ways. The first is more or less a full solution to the above question and the second one is a solution to an analogous question when we replace primitive sub-lattices with a more general object: rational flag.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The talk should be accessible to graduate students and no prior knowledge will be assumed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker: Yakov Karasik (Technion) Topic: Counting rational flags of $Z^n$ Place: This is an online seminar. Please email Yuval Ginosar \u201cginosar at math dot haifa dot ac dot il\u201d for the Zoom ID and password. Date: Tuesday, May 4, 2021&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2027\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7,1],"tags":[],"class_list":["post-2027","post","type-post","status-publish","format-standard","hentry","category-colloquium","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2027","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\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2027"}],"version-history":[{"count":2,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2027\/revisions"}],"predecessor-version":[{"id":2117,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2027\/revisions\/2117"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2027"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2027"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2027"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}