{"id":1511,"date":"2025-12-05T11:21:22","date_gmt":"2025-12-05T19:21:22","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1511"},"modified":"2025-12-10T14:50:11","modified_gmt":"2025-12-10T22:50:11","slug":"a-microlocal-calculus-on-filtered-manifolds","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/12\/05\/a-microlocal-calculus-on-filtered-manifolds\/","title":{"rendered":"A Microlocal Calculus on Filtered Manifolds"},"content":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0<b>December 9nd<\/b>, will be at\u00a0<strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>Steven Flynn<\/p>\n<p><strong>Abstract: <\/strong>Sub-Riemannian geometries arise naturally in quantum mechanics and control theory, yet fundamental questions about quantum dynamics remain open, suggesting that new microlocal tools are needed to extend classical results to these singular geometries.<\/p>\n<p>I will present a pseudodifferential calculus for filtered manifolds with operator-valued symbols built using representation theory of nilpotent groups. The key innovation is an explicit quantization procedure for noncommutative symbols adapted to the filtration, extending the Van Erp-Yuncken calculus while maintaining essential properties: closure under composition, parametrices, and Sobolev continuity.<\/p>\n<p>This framework enables systematic microlocal analysis on equiregular sub-Riemannian manifolds. This is joint work with V\u00e9ronique Fischer and Clotilde Fermanian-Kammerer.<strong><br \/>\n<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0December 9nd, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Steven Flynn Abstract: Sub-Riemannian geometries arise naturally in quantum mechanics and control theory, yet fundamental questions about quantum dynamics remain open, suggesting that new microlocal tools are needed to extend classical results to these singular geometries. I will present a pseudodifferential calculus for filtered manifolds [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25,1],"tags":[],"class_list":["post-1511","post","type-post","status-publish","format-standard","hentry","category-fall-2025","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1511","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1511"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1511\/revisions"}],"predecessor-version":[{"id":1512,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1511\/revisions\/1512"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}