{"id":14146,"date":"2024-04-11T15:17:11","date_gmt":"2024-04-11T20:17:11","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=14146"},"modified":"2024-04-15T08:37:46","modified_gmt":"2024-04-15T13:37:46","slug":"colloquium-prof-roger-howe","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/","title":{"rendered":"Colloquium: Prof. Roger Howe"},"content":{"rendered":"

\"\"Mathematics around the Heisenberg Group<\/h1>\n

Prof. Roger Howe
\nProfessor Emeritus<\/em>
\nYale University<\/p>\n

In the mid 1920s, Werner Heisenberg formulated the CCR \u2013 canonical commutation relations \u2013 describing the relationship between the operations of measuring position and of measuring momentum of a particle in quantum mechanics. These have been fundamental to the later, dramatically successful development of subatomic physics. Shortly after Heisenberg\u2019s work, Hermann Weyl pointed out that the CCR defined the relations of a Lie algebra, whose associated group is a two-step nilpotent group with one dimensional center. Today, this group (and its increasingly large set of cousins) is known as the \u201cHeisenberg group\u201d. Over the remainder of the 20th century, appreciation grew of the fundamental role of the Heisenberg group in disparate mathematical topics, including harmonic analysis, partial differential equations, invariant theory and representation theory, in both finite and infinite dimensions. This talk will review and attempt to summarize some of the manifold connections between these topics that are mediated by the Heisenberg group<\/p>\n","protected":false},"excerpt":{"rendered":"

Mathematics around the Heisenberg Group Prof. Roger Howe Professor Emeritus Yale University In the mid 1920s, Werner Heisenberg formulated the CCR \u2013 canonical commutation relations \u2013 describing the relationship between the operations of measuring position and of measuring momentum of …<\/p>\n","protected":false},"author":4217,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","uwm_wg_additional_authors":[]},"tags":[],"tribe_events_cat":[41],"class_list":["post-14146","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-colloquia","cat_colloquia"],"yoast_head":"\nMathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Colloquium: Prof. Roger Howe\" \/>\n<meta property=\"og:description\" content=\"Mathematics around the Heisenberg Group Prof. Roger Howe Professor Emeritus Yale University In the mid 1920s, Werner Heisenberg formulated the CCR \u2013 canonical commutation relations \u2013 describing the relationship between the operations of measuring position and of measuring momentum of …\" \/>\n<meta property=\"og:url\" content=\"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2024-04-15T13:37:46+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/04\/BANNER_HOWE.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-prof-roger-howe\\\/\",\"url\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-prof-roger-howe\\\/\",\"name\":\"Colloquium: Prof. Roger Howe - Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-prof-roger-howe\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-prof-roger-howe\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/uwm.edu\\\/math\\\/wp-content\\\/uploads\\\/sites\\\/112\\\/2024\\\/04\\\/BANNER_HOWE.jpg\",\"datePublished\":\"2024-04-11T20:17:11+00:00\",\"dateModified\":\"2024-04-15T13:37:46+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-prof-roger-howe\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-prof-roger-howe\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-prof-roger-howe\\\/#primaryimage\",\"url\":\"https:\\\/\\\/uwm.edu\\\/math\\\/wp-content\\\/uploads\\\/sites\\\/112\\\/2024\\\/04\\\/BANNER_HOWE.jpg\",\"contentUrl\":\"https:\\\/\\\/uwm.edu\\\/math\\\/wp-content\\\/uploads\\\/sites\\\/112\\\/2024\\\/04\\\/BANNER_HOWE.jpg\",\"width\":984,\"height\":504},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-prof-roger-howe\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\",\"item\":\"https:\\\/\\\/uwm.edu\\\/math\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Events\",\"item\":\"https:\\\/\\\/uwm.edu\\\/math\\\/events\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Colloquia\",\"item\":\"https:\\\/\\\/uwm.edu\\\/math\\\/events\\\/category\\\/colloquia\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Colloquium: Prof. Roger Howe\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/#website\",\"url\":\"https:\\\/\\\/uwm.edu\\\/math\\\/\",\"name\":\"Mathematical Sciences\",\"description\":\"UW-Milwaukee\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/uwm.edu\\\/math\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Mathematical Sciences","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/","og_locale":"en_US","og_type":"article","og_title":"Colloquium: Prof. Roger Howe","og_description":"Mathematics around the Heisenberg Group Prof. Roger Howe Professor Emeritus Yale University In the mid 1920s, Werner Heisenberg formulated the CCR \u2013 canonical commutation relations \u2013 describing the relationship between the operations of measuring position and of measuring momentum of …","og_url":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/","og_site_name":"Mathematical Sciences","article_modified_time":"2024-04-15T13:37:46+00:00","og_image":[{"url":"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/04\/BANNER_HOWE.jpg","type":"","width":"","height":""}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/","url":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/","name":"Colloquium: Prof. Roger Howe - Mathematical Sciences","isPartOf":{"@id":"https:\/\/uwm.edu\/math\/#website"},"primaryImageOfPage":{"@id":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/#primaryimage"},"image":{"@id":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/#primaryimage"},"thumbnailUrl":"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/04\/BANNER_HOWE.jpg","datePublished":"2024-04-11T20:17:11+00:00","dateModified":"2024-04-15T13:37:46+00:00","breadcrumb":{"@id":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/#primaryimage","url":"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/04\/BANNER_HOWE.jpg","contentUrl":"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/04\/BANNER_HOWE.jpg","width":984,"height":504},{"@type":"BreadcrumbList","@id":"https:\/\/uwm.edu\/math\/event\/colloquium-prof-roger-howe\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"","item":"https:\/\/uwm.edu\/math\/"},{"@type":"ListItem","position":2,"name":"Events","item":"https:\/\/uwm.edu\/math\/events\/"},{"@type":"ListItem","position":3,"name":"Colloquia","item":"https:\/\/uwm.edu\/math\/events\/category\/colloquia\/"},{"@type":"ListItem","position":4,"name":"Colloquium: Prof. Roger Howe"}]},{"@type":"WebSite","@id":"https:\/\/uwm.edu\/math\/#website","url":"https:\/\/uwm.edu\/math\/","name":"Mathematical Sciences","description":"UW-Milwaukee","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/uwm.edu\/math\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"acf":[],"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tribe_events\/14146","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tribe_events"}],"about":[{"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/types\/tribe_events"}],"author":[{"embeddable":true,"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/users\/4217"}],"version-history":[{"count":2,"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tribe_events\/14146\/revisions"}],"predecessor-version":[{"id":14156,"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tribe_events\/14146\/revisions\/14156"}],"wp:attachment":[{"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/media?parent=14146"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tags?post=14146"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tribe_events_cat?post=14146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}