{"id":2473,"date":"2025-09-29T09:20:23","date_gmt":"2025-09-29T09:20:23","guid":{"rendered":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/?page_id=2473"},"modified":"2026-01-14T10:48:54","modified_gmt":"2026-01-14T10:48:54","slug":"ws-25-26","status":"publish","type":"page","link":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/learning-seminar\/ws-25-26\/","title":{"rendered":"WS 25\/26: The inverse function theorem of Nash and Moser"},"content":{"rendered":"\n<p>We shall meet on Tuesdays from 14h to 15:30h in \u00dcbungsraum 1 (-119).<br>Here is a tentative schedule:<\/p>\n\n\n\n<p>14.10. (Christoph) <strong>Introduction to Locally Convex Vector Spaces<\/strong> [Ham82, \u00a7I.1\u2013I.2], [Sch22, \u00a71.1\u20131.4].<\/p>\n\n\n\n<p>21.10 (Christoph) <strong>Differential Calculus in Locally Convex Vector Spaces<\/strong> [Ham82, \u00a7I.3], [Sch22, \u00a71.1\u20131.4].<\/p>\n\n\n\n<p>28.10. <em>No seminar due to the Workshop \u2018Who is afraid of infinite dimensions?\u2019 in Lyon.<\/em><\/p>\n\n\n\n<p>04.11. (Jorn) <strong>Infinite-Dimensional Manifolds<\/strong> [Ham82, \u00a7I.4.1\u2013I.4.4], [Sch22, \u00a71.5\u20131.7].<\/p>\n\n\n\n<p>11.11. <em>No seminar due to Elfter im Elften.<\/em><\/p>\n\n\n\n<p>18.11. (Jorn) <strong>Spaces and Manifolds of Smooth Maps<\/strong> [Sch22, \u00a72].<\/p>\n\n\n\n<p>25.11. (Nico) <strong>Infinite-Dimensional Lie Groups<\/strong> [Ham82, \u00a7I.4.6], [Sch22, \u00a73].<\/p>\n\n\n\n<p>02.12. (Christoph) <strong>The inverse function theorem for Banach spaces<\/strong> [Ham82, \u00a7I.5].<\/p>\n\n\n\n<p>09.12. (Rodrigo) <strong>The Nash-Moser Category I<\/strong> [Ham82, \u00a7II.1\u2013II.2].<\/p>\n\n\n\n<p>16.12. (Rodrigo) <strong>The Nash-Moser Category II<\/strong> [Ham82, \u00a7II.2\u2013II.3].<\/p>\n\n\n\n<p>13.01. (Christoph) <strong>The Proof of the Nash-Moser theorem<\/strong> [Ham82, \u00a7III.1].<\/p>\n\n\n\n<p>20.01. (Jorn) <strong>Applications of the Nash-Moser theorem<\/strong> [Ham82, \u00a7III.2].<\/p>\n\n\n\n<p>27.01. (Nico) <strong>Volume-preserving diffeomorphisms<\/strong> [Ham82, \u00a7III.2.5].<\/p>\n\n\n\n<p>03.02. <strong>T.B.D.<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<style>\n    details {\n        margin-top: 10px; \/* Adjust this value to decrease space above *\/\n        margin-bottom: 30px; \/* Adjust this value to control space below *\/\n    }\n    summary {\n        display: flex;\n        align-items: center; \/* Center the items vertically *\/\n        cursor: pointer; \/* Change cursor to hand when hovering *\/\n    }\n    .indicator {\n        display: inline-block;\n        width: 0;\n        height: 0;\n        border-top: 3px solid transparent;\n        border-bottom: 3px solid transparent;\n        border-left: 6px solid black; \/* Color of the triangle *\/\n        transition: transform 0.3s ease;\n        margin-right: 5px;\n    }\n    details[open] .indicator {\n        transform: rotate(90deg); \/* Rotate to point down when open *\/\n    }\n    .par-ind-spaced {\n        text-indent: 20px; \/* Indentation *\/\n        margin-top: 20px;\n        margin-bottom: -10px; \/* Larger line separation *\/\n    }\n<\/style>\n\n<details>\n    <summary>\n        <span class=\"indicator\"><\/span>\n\nReferences\n\n    <\/summary>\n    <p class=\"par-ind-spaced\">\n\n[Ham82] Richard S. Hamilton. \u2018The inverse function theorem of Nash and Moser\u2019. Bull. Am. Math. Soc., New Ser., 7:65\u2013222, 1982.\n\n    <\/p>\n    <p class=\"par-ind-spaced\">\n\n[Sch22] Alexander Schmeding. \u2018An Introduction to Infinite-Dimensional Differential Geometry\u2019. Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2022.\n\n    <\/p>\n<\/details>\n","protected":false},"excerpt":{"rendered":"<p>We shall meet on Tuesdays from 14h to 15:30h in \u00dcbungsraum 1 (-119).Here is a tentative schedule: 14.10. (Christoph) Introduction to Locally Convex Vector Spaces [Ham82, \u00a7I.1\u2013I.2], [Sch22, \u00a71.1\u20131.4]. 21.10 (Christoph) Differential Calculus in Locally Convex Vector Spaces [Ham82, \u00a7I.3], [Sch22, \u00a71.1\u20131.4]. 28.10. No seminar due to the Workshop \u2018Who is afraid of infinite dimensions?\u2019 &hellip; <a href=\"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/learning-seminar\/ws-25-26\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;WS 25\/26: The inverse function theorem of Nash and Moser&#8221;<\/span><\/a><\/p>\n","protected":false},"author":8,"featured_media":0,"parent":644,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2473","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/pages\/2473","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/comments?post=2473"}],"version-history":[{"count":6,"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/pages\/2473\/revisions"}],"predecessor-version":[{"id":2513,"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/pages\/2473\/revisions\/2513"}],"up":[{"embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/pages\/644"}],"wp:attachment":[{"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/media?parent=2473"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}