{"id":1622,"date":"2020-01-06T12:11:08","date_gmt":"2020-01-06T10:11:08","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=1622"},"modified":"2020-01-16T16:43:50","modified_gmt":"2020-01-16T14:43:50","slug":"this-week-thursday-at-1100-u-haifa-topology-geometry-seminar-on-january-9-2020","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=1622","title":{"rendered":"This week, Thursday at 11:00, U. Haifa Topology &#038; Geometry seminar on January 9, 2020"},"content":{"rendered":"<p><strong><u>Geometry\u00a0&amp; Topology Seminar<\/u><\/strong><\/p>\n<p>Speaker:\u00a0\u00a0Shamgar\u00a0Gurevich\u00a0(Wisconsin-Madison)<\/p>\n<p>Topic:\u00a0\u00a0Harmonic Analysis on GL(n) over Finite Fields.<\/p>\n<p>Place:\u00a0 Room 614 in the Science &amp; Education Building<\/p>\n<p>Time:\u00a0 \u00a011:00<\/p>\n<p>Date:\u00a0 Thursday, January 9,\u00a0 2020<\/p>\n<p>&nbsp;<\/p>\n<p><strong><u>Abstract<\/u><\/strong><strong><u>:<\/u><\/strong><\/p>\n<p>There are many formulas that express interesting properties of a finite group G in terms of sums over its characters.\u00a0For\u00a0estimating these sums, one of the most salient quantities to understand is the\u00a0<strong>character ratio<\/strong>:<\/p>\n<p>&nbsp;<\/p>\n<p>Trace(\u03c1(g)) \/ dim(\u03c1),<\/p>\n<p>&nbsp;<\/p>\n<p>for an irreducible representation \u03c1 of G and an element g of G. For example, Diaconis and Shahshahani stated a formula\u00a0of the mentioned type for analyzing certain random walks on G.<\/p>\n<p>Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that\u00a0provides strong information on the character ratio. We call this invariant\u00a0<strong>rank<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n<p>Rank suggests a new organization of representations based on the very few \u201cSmall\u201d ones. This stands in contrast to\u00a0Harish-Chandra\u2019s \u201cphilosophy of cusp forms\u201d (P-of-CF), which is (since the 60s) the main organization principle, and is\u00a0based on the (huge collection) of \u201cLarge\u201d representations.<\/p>\n<p>This talk will discuss the notion of rank for the group GL(n) over finite fields, demonstrate how it controls the character\u00a0ratio, and explain how one can apply the results to verify mixing time and rate for random walks.<\/p>\n<p>This is joint work with\u00a0<strong>Roger Howe<\/strong>\u00a0(Yale and Texas A&amp;M). The numerics for this work was carried by\u00a0<strong>Steve Goldstein<\/strong>\u00a0(Madison).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Geometry\u00a0&amp; Topology Seminar Speaker:\u00a0\u00a0Shamgar\u00a0Gurevich\u00a0(Wisconsin-Madison) Topic:\u00a0\u00a0Harmonic Analysis on GL(n) over Finite Fields. Place:\u00a0 Room 614 in the Science &amp; Education Building Time:\u00a0 \u00a011:00 Date:\u00a0 Thursday, January 9,\u00a0 2020 &nbsp; Abstract: There are many formulas that express interesting properties of a finite&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=1622\">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-1622","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\/1622","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=1622"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1622\/revisions"}],"predecessor-version":[{"id":1623,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/1622\/revisions\/1623"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1622"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1622"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1622"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}