{"id":16607,"date":"2026-02-02T10:38:13","date_gmt":"2026-02-02T16:38:13","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=16607"},"modified":"2026-02-02T10:38:13","modified_gmt":"2026-02-02T16:38:13","slug":"colloquium-dr-joseph-rennie","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/colloquium-dr-joseph-rennie\/","title":{"rendered":"Colloquium: Dr. Joseph Rennie"},"content":{"rendered":"

(Higher) Categorical Galois Theory for the Aspiring Mathematician<\/strong><\/p>\n

Here we focus on the function\/motivation of specific structures (most likely new to the audience) in high-level mathematics with the aim of highlighting major themes in the broader canvas of modern mathematics. Specifically, Galois Theoretic ideas emerge across disciplines, all as instances of a single theorem in (higher) category theory. This talk uses that idea to motivate a journey through three main themes relevant to any area:<\/p>\n

    \n
  1. The ubiquity of presheaf localizations<\/li>\n
  2. The concept of a classifying object<\/li>\n
  3. The pervasiveness of Algebro-Geometric duality<\/li>\n<\/ol>\n

    In some parts, I will use categorical-theoretic language not with the expectation that people speak the language, but rather as a demonstration of the beauty of the perspective gained by acquiring fluency. (What better way to motivate oneself to learn a new language than to listen to some of its poetry?)<\/p>\n

    This talk also serves as an onboarding for those interested in research projects on this topic. Though the talk should also inspire those who have no interest in category-theoretic research.<\/p>\n","protected":false},"excerpt":{"rendered":"

    (Higher) Categorical Galois Theory for the Aspiring Mathematician Here we focus on the function\/motivation of specific structures (most likely new to the audience) in high-level mathematics with the aim of highlighting major themes in the broader canvas of modern mathematics. …<\/p>\n","protected":false},"author":19040,"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-16607","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-dr-joseph-rennie\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Colloquium: Dr. Joseph Rennie\" \/>\n<meta property=\"og:description\" content=\"(Higher) Categorical Galois Theory for the Aspiring Mathematician Here we focus on the function\/motivation of specific structures (most likely new to the audience) in high-level mathematics with the aim of highlighting major themes in the broader canvas of modern mathematics. …\" \/>\n<meta property=\"og:url\" content=\"https:\/\/uwm.edu\/math\/event\/colloquium-dr-joseph-rennie\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathematical Sciences\" \/>\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-dr-joseph-rennie\\\/\",\"url\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-dr-joseph-rennie\\\/\",\"name\":\"Colloquium: Dr. Joseph Rennie - Mathematical Sciences\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/#website\"},\"datePublished\":\"2026-02-02T16:38:13+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-dr-joseph-rennie\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-dr-joseph-rennie\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-dr-joseph-rennie\\\/#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: Dr. Joseph Rennie\"}]},{\"@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-dr-joseph-rennie\/","og_locale":"en_US","og_type":"article","og_title":"Colloquium: Dr. Joseph Rennie","og_description":"(Higher) Categorical Galois Theory for the Aspiring Mathematician Here we focus on the function\/motivation of specific structures (most likely new to the audience) in high-level mathematics with the aim of highlighting major themes in the broader canvas of modern mathematics. …","og_url":"https:\/\/uwm.edu\/math\/event\/colloquium-dr-joseph-rennie\/","og_site_name":"Mathematical Sciences","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-dr-joseph-rennie\/","url":"https:\/\/uwm.edu\/math\/event\/colloquium-dr-joseph-rennie\/","name":"Colloquium: Dr. Joseph Rennie - Mathematical Sciences","isPartOf":{"@id":"https:\/\/uwm.edu\/math\/#website"},"datePublished":"2026-02-02T16:38:13+00:00","breadcrumb":{"@id":"https:\/\/uwm.edu\/math\/event\/colloquium-dr-joseph-rennie\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/uwm.edu\/math\/event\/colloquium-dr-joseph-rennie\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/uwm.edu\/math\/event\/colloquium-dr-joseph-rennie\/#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: Dr. Joseph Rennie"}]},{"@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\/16607","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\/19040"}],"version-history":[{"count":1,"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tribe_events\/16607\/revisions"}],"predecessor-version":[{"id":16608,"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tribe_events\/16607\/revisions\/16608"}],"wp:attachment":[{"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/media?parent=16607"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tags?post=16607"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/uwm.edu\/math\/wp-json\/wp\/v2\/tribe_events_cat?post=16607"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}