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{background:#EDF4EC;color:#2D6A4F;}\n.nb-badge.default {background:#F0EBE0;color:#7A6E60;}\n\n.grp-placeholder{padding:1.5rem 1.8rem;background:#F0EBE0;border:1px dashed var(--rule);font-family:var(--garamond);font-style:italic;font-size:.95rem;color:#9A8E80;line-height:1.65;display:flex;align-items:flex-start;gap:.8rem;}\n.grp-placeholder-icon{font-size:1.1rem;margin-top:.1rem;flex-shrink:0;}\n.grp-lower-grid{display:grid;grid-template-columns:1fr 1fr;gap:0 3rem;margin-top:0;}\n\n\/* \u2500\u2500 Skeleton \u2500\u2500 *\/\n.nb-skel{padding:.75rem 0;display:flex;gap:.8rem;}\n.nb-skel-box{background:rgba(26,22,16,.07);border-radius:2px;animation:nb-pulse 1.5s infinite;}\n.nb-skel-d{height:18px;width:52px;flex-shrink:0;}\n.nb-skel-l1{height:9px;width:35%;margin-bottom:5px;}\n.nb-skel-l2{height:13px;width:85%;}\n@keyframes nb-pulse{0%,100%{opacity:.4}50%{opacity:.7}}\n\n@media(max-width:680px){\n .grp-hero{padding:2rem 1.5rem 1.8rem;}\n .grp-body{padding:2rem 1.5rem;}\n .grp-members{grid-template-columns:1fr;}\n .grp-lower-grid{grid-template-columns:1fr;gap:2rem;}\n .ga-item{grid-template-columns:44px 1fr;}\n}\n<\/style>\n\n<div class=\"grp-block\">\n <div class=\"grp-accent geometry\"><\/div>\n\n <div class=\"grp-hero geometry\">\n <a class=\"grp-hero-back\" href=\"\/index.php\/research\/\">\n <svg viewBox=\"0 0 10 10\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"1.5\"><path d=\"M7 1L3 5l4 4\"\/><\/svg>\n Research Groups\n <\/a>\n <div class=\"grp-hero-tag\">Mathematics Research Center \u00b7 ASOIU<\/div>\n <h1>Noncommutative Geometry Research Group<\/h1>\n <p class=\"grp-hero-sub\">Noncommutative geometry, associative algebras, and quantum groups.<\/p>\n <\/div>\n\n <div class=\"grp-body\">\n <div class=\"grp-label\">About the Group<\/div>\n <div class=\"grp-desc\">\n <p>The Noncommutative Geometry Group focuses on the generalization of results, tools, and constructions from both differential geometry and algebraic geometry to the noncommutative setting. Using methods primarily from category theory and homological algebra, this has led to developments on the noncommutative analogues of jets, differential operators, higher order connections, quantization, Spencer cohomology, de Rham cohomology, and diffeomorphisms. The group also investigates new phenomena which appear only in the noncommutative setting, novel insights into the classical setting which arise when viewed from a noncommutative perspective, and applications of the general theory to problems in mathematical physics.<\/p>\n <\/div>\n\n <div class=\"grp-label grp-mt\">Members<\/div>\n <div class=\"grp-members\">\n <a class=\"grp-member-card\" href=\"\/index.php\/keeganflood\/\">\n <div class=\"grp-member-placeholder\">KF<\/div>\n <div class=\"grp-member-info\">\n <div class=\"grp-member-name\">Keegan Flood<\/div>\n <div class=\"grp-member-role\">Researcher<\/div>\n <\/div>\n <\/a>\n <\/div>\n\n <div class=\"grp-lower-grid\">\n \n <div>\n <div class=\"grp-label grp-mt\">Recent Activities<\/div>\n <div id=\"ga-list-geometry\">\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <\/div>\n <\/div>\n\n \n <div>\n <div class=\"grp-label grp-mt\">Announcements<\/div>\n <div id=\"ga-ann-geometry\">\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n<\/div>\n\n<script>\n(function(){\n var SITE = window.location.origin;\n var GROUP_TAG_ID = 25; \/\/ Tag ID for Geometry\/NCG[cite: 1]\n var MONTHS = ['Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec'];\n\n var SEMINAR_CATS = [6, 7, 8, 15];\n var SEMINAR_MAP = {\n 6: {cls:'seminar', label:'General Seminar'},\n 7: {cls:'seminar', label:'Research Seminar'},\n 8: {cls:'seminar', label:'Student Seminar'},\n 15: {cls:'conference', label:'Conference'},\n 'default': {cls:'default', label:'Seminar'}\n };\n\n var NEWS_CATS = [19, 20, 21, 22, 23, 28];\n var NEWS_MAP = {\n 19: {cls:'publication', label:'Publication'},\n 20: {cls:'seminar-abroad', label:'Seminar abroad'},\n 21: {cls:'new-member', label:'New member'},\n 23: {cls:'award', label:'Award'},\n 28: {cls:'milestone', label:'Milestone'},\n 22: {cls:'visitor', label:'Visitor'},\n 'default': {cls:'default', label:'News'}\n };\n\n function getBadge(cats, map){\n if(cats) for(var i=0;i<cats.length;i++) if(map[cats[i]]) return map[cats[i]];\n return map['default'];\n }\n\n function renderList(posts, map, listEl, emptyMsg){\n if(!posts.length){\n listEl.innerHTML = '<div class=\"grp-placeholder\"><span class=\"grp-placeholder-icon\">\ud83d\udcc5<\/span>' + emptyMsg + '<\/div>';\n return;\n }\n var html = '<ul class=\"ga-list\">';\n posts.forEach(function(p){\n var d = new Date(p.date);\n var badge = getBadge(p.categories, map);\n var title = p.title.rendered.replace(\/<[^>]+>\/g,'');\n html += '<li class=\"ga-item\"><div class=\"ga-date-box\"><span class=\"ga-date-day\">' + d.getDate() + '<\/span><span class=\"ga-date-mon\">' + MONTHS[d.getMonth()] + '<\/span><\/div>' +\n '<div class=\"ga-content\"><span class=\"nb-badge ' + badge.cls + '\">' + badge.label + '<\/span><div class=\"ga-title\">' +\n (p.link ? 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About the Group The Noncommutative Geometry Group focuses on the generalization of results, tools, and constructions from both differential geometry and algebraic geometry to the noncommutative setting. 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{"id":67,"date":"2026-04-14T03:28:55","date_gmt":"2026-04-14T03:28:55","guid":{"rendered":"https:\/\/mrc-baku.org\/?page_id=67"},"modified":"2026-05-01T18:33:25","modified_gmt":"2026-05-01T18:33:25","slug":"geometry","status":"publish","type":"page","link":"https:\/\/mrc-baku.org\/index.php\/geometry\/","title":{"rendered":"MRC – Geometry"},"content":{"rendered":"\n\n\n\n\n\nGeometry Research Group \u2014 Mathematics Research Center<\/title>\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=EB+Garamond:ital,wght@0,400;0,500;0,600;1,400;1,500&family=DM+Mono:wght@300;400;500&family=Outfit:wght@300;400;500;600&display=swap\" rel=\"stylesheet\">\n<script>MathJax = { tex: { inlineMath: [['\\\\(','\\\\)']] } };<\/script>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjax@3\/es5\/tex-chtml.js\" async><\/script>\n<style>body{background:#eee;padding:2rem;margin:0;}<\/style>\n<\/head>\n<body>\n\n\n<style>\n:root {\n 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.grp-members{grid-template-columns:1fr;}\n .grp-lower-grid{grid-template-columns:1fr;gap:2rem;}\n .ga-item{grid-template-columns:44px 1fr;}\n}\n<\/style>\n\n<div class=\"grp-block\">\n <div class=\"grp-accent geometry\"><\/div>\n\n <div class=\"grp-hero geometry\">\n <a class=\"grp-hero-back\" href=\"\/index.php\/research\/\">\n <svg viewBox=\"0 0 10 10\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"1.5\"><path d=\"M7 1L3 5l4 4\"\/><\/svg>\n Research Groups\n <\/a>\n <div class=\"grp-hero-tag\">Mathematics Research Center \u00b7 ASOIU<\/div>\n <h1>Noncommutative Geometry Research Group<\/h1>\n <p class=\"grp-hero-sub\">Noncommutative geometry, associative algebras, and quantum groups.<\/p>\n <\/div>\n\n <div class=\"grp-body\">\n <div class=\"grp-label\">About the Group<\/div>\n <div class=\"grp-desc\">\n <p>The Noncommutative Geometry Group focuses on the generalization of results, tools, and constructions from both differential geometry and algebraic geometry to the noncommutative setting. Using methods primarily from category theory and homological algebra, this has led to developments on the noncommutative analogues of jets, differential operators, higher order connections, quantization, Spencer cohomology, de Rham cohomology, and diffeomorphisms. The group also investigates new phenomena which appear only in the noncommutative setting, novel insights into the classical setting which arise when viewed from a noncommutative perspective, and applications of the general theory to problems in mathematical physics.<\/p>\n <\/div>\n\n <div class=\"grp-label grp-mt\">Members<\/div>\n <div class=\"grp-members\">\n <a class=\"grp-member-card\" href=\"\/index.php\/keeganflood\/\">\n <div class=\"grp-member-placeholder\">KF<\/div>\n <div class=\"grp-member-info\">\n <div class=\"grp-member-name\">Keegan Flood<\/div>\n <div class=\"grp-member-role\">Researcher<\/div>\n <\/div>\n <\/a>\n <\/div>\n\n <div class=\"grp-lower-grid\">\n \n <div>\n <div class=\"grp-label grp-mt\">Recent Activities<\/div>\n <div id=\"ga-list-geometry\">\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <\/div>\n <\/div>\n\n \n <div>\n <div class=\"grp-label grp-mt\">Announcements<\/div>\n <div id=\"ga-ann-geometry\">\n <div class=\"nb-skel\"><div class=\"nb-skel-box nb-skel-d\"><\/div><div style=\"flex:1\"><div class=\"nb-skel-box nb-skel-l1\"><\/div><div class=\"nb-skel-box nb-skel-l2\"><\/div><\/div><\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n<\/div>\n\n<script>\n(function(){\n var SITE = window.location.origin;\n var GROUP_TAG_ID = 25; \/\/ Tag ID for Geometry\/NCG[cite: 1]\n var MONTHS = ['Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec'];\n\n var SEMINAR_CATS = [6, 7, 8, 15];\n var SEMINAR_MAP = {\n 6: {cls:'seminar', label:'General Seminar'},\n 7: {cls:'seminar', label:'Research Seminar'},\n 8: {cls:'seminar', label:'Student Seminar'},\n 15: {cls:'conference', label:'Conference'},\n 'default': {cls:'default', label:'Seminar'}\n };\n\n var NEWS_CATS = [19, 20, 21, 22, 23, 28];\n var NEWS_MAP = {\n 19: {cls:'publication', label:'Publication'},\n 20: {cls:'seminar-abroad', label:'Seminar abroad'},\n 21: {cls:'new-member', label:'New member'},\n 23: {cls:'award', label:'Award'},\n 28: {cls:'milestone', label:'Milestone'},\n 22: {cls:'visitor', label:'Visitor'},\n 'default': {cls:'default', label:'News'}\n };\n\n function getBadge(cats, map){\n if(cats) for(var i=0;i<cats.length;i++) if(map[cats[i]]) return map[cats[i]];\n return map['default'];\n }\n\n function renderList(posts, map, listEl, emptyMsg){\n if(!posts.length){\n listEl.innerHTML = '<div class=\"grp-placeholder\"><span class=\"grp-placeholder-icon\">\ud83d\udcc5<\/span>' + emptyMsg + '<\/div>';\n return;\n }\n var html = '<ul class=\"ga-list\">';\n posts.forEach(function(p){\n var d = new Date(p.date);\n var badge = getBadge(p.categories, map);\n var title = p.title.rendered.replace(\/<[^>]+>\/g,'');\n html += '<li class=\"ga-item\"><div class=\"ga-date-box\"><span class=\"ga-date-day\">' + d.getDate() + '<\/span><span class=\"ga-date-mon\">' + MONTHS[d.getMonth()] + '<\/span><\/div>' +\n '<div class=\"ga-content\"><span class=\"nb-badge ' + badge.cls + '\">' + badge.label + '<\/span><div class=\"ga-title\">' +\n (p.link ? 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About the Group The Noncommutative Geometry Group focuses on the generalization of results, tools, and constructions from both differential geometry and algebraic geometry to the noncommutative setting. Using methods primarily […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-67","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages\/67","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/comments?post=67"}],"version-history":[{"count":8,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages\/67\/revisions"}],"predecessor-version":[{"id":594,"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/pages\/67\/revisions\/594"}],"wp:attachment":[{"href":"https:\/\/mrc-baku.org\/index.php\/wp-json\/wp\/v2\/media?parent=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}