{"id":19489,"date":"2020-10-06T11:56:40","date_gmt":"2020-10-06T15:56:40","guid":{"rendered":"https:\/\/carleton.ca\/math\/?p=19489"},"modified":"2020-10-06T11:57:11","modified_gmt":"2020-10-06T15:57:11","slug":"joint-colloquium-carleton-university-university-of-ottawa-18","status":"publish","type":"post","link":"https:\/\/carleton.ca\/math\/2020\/joint-colloquium-carleton-university-university-of-ottawa-18\/","title":{"rendered":"Joint Colloquium: Carleton University \u2013 University of Ottawa"},"content":{"rendered":"<p>Date:\u00a0 Friday, October 9, 2020<br \/>\nTime:\u00a0 4:00 pm<br \/>\nPlace:\u00a0 ZOOM<br \/>\nSpeaker:\u00a0 Shamgar Gurevitch (University of Wisconsin)<br \/>\nTitle:\u00a0 Harmonic Analysis on GL(n) over finite fields<\/p>\n<p><\/p>\n<p>Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For estimating these sums, one of the most salient quantities to understand is the character ratio: Trace(\u00f1(g)) \/ dim(\u00f1), for an irreducible representation \u00f1 of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G. In 2015, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio.<\/p>\n<p>We call this invariant rank. Rank suggests a new organization of representations based on the very few &#8220;small&#8221; ones. This stands in contrast to Harish-Chandra&#8217;s &#8220;philosophy of cusp forms&#8221;, which is (since the 60s) the main organization principle, and is based on the (huge collection) of &#8220;LARGE&#8221; representations. This talk will discuss the notion of rank for the group GL(n) over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for random walks. This is joint work with Roger Howe (Yale and Texas A&amp;M). The numerics for this work was carried by Steve Goldstein (Madison).<\/p>\n<p>Join Zoom Meeting:<\/p>\n<p><a href=\"https:\/\/uottawa-ca.zoom.us\/j\/93104654430?pwd=RVZLN3ROMkNObW5aQ3Jva0N4VVRnUT09\">https:\/\/uottawa-ca.zoom.us\/j\/93104654430?pwd=RVZLN3ROMkNObW5aQ3Jva0N4VVRnUT09<\/a><\/p>\n<p><\/p>\n<p>Meeting ID: 931 0465 4430<\/p>\n<p>Passcode: pP73dd<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Date:\u00a0 Friday, October 9, 2020 Time:\u00a0 4:00 pm Place:\u00a0 ZOOM Speaker:\u00a0 Shamgar Gurevitch (University of Wisconsin) Title:\u00a0 Harmonic Analysis on GL(n) over finite fields Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For estimating these sums, one of the most salient quantities [&hellip;]<\/p>\n","protected":false},"author":18,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[14,1],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - 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