{"id":1687,"date":"2025-02-11T16:16:46","date_gmt":"2025-02-11T16:16:46","guid":{"rendered":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/?page_id=1687"},"modified":"2025-07-10T07:42:13","modified_gmt":"2025-07-10T07:42:13","slug":"ss-25","status":"publish","type":"page","link":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/learning-seminar\/ss-25\/","title":{"rendered":"SS 25: Deformation Quantisation"},"content":{"rendered":"\n<p class=\"par-indented\">In the summer semester 2025, we will discuss deformation quantization in the Poisson geometry reading seminar. Formal deformation quantization is a mathematical framework that describes the transition from classical to quantum mechanics by deforming the algebra of functions on phase space. It replaces the classical pointwise product with a noncommutative star product parameterized by Planck\u2019s constant, capturing quantum effects within a formal expansion. This approach provides a systematic way to study the relationship between classical and quantum mechanics while connecting to areas like symplectic geometry and Poisson structures.<\/p>\n\n\n\n<p>We meet on Tuesdays at 14:00h in Seminarraum 1. Here is a tentative schedule:<br><strong>Attention:<\/strong> Due to some scheduling issues, it has been decided that, from the <strong>22<sup>nd<\/sup> of April onwards<\/strong>, the seminar will take place at <strong>16h<\/strong> in <strong>Stefan Cohn-Vossen Raum (313)<\/strong>.<br><\/p>\n\n\n\n<p>08.04. (Jorn) <strong>Introduction and star products<\/strong> [Esp14, \u00a73.1\u20133.3], [Wal07, \u00a76.1].<\/p>\n\n\n\n<p>15.04 (Christoph) <strong>Quantizations of linear Poisson structures<\/strong> [Sch22, \u00a73.3], [Gut83].<\/p>\n\n\n\n<p>22.04. (Christoph) <strong>Deformations and differential graded Lie algebras<\/strong> [Esp14, \u00a73.4], [Wal07, \u00a76.2.3], [CKTB05, \u00a72.1].<\/p>\n\n\n\n<p>29.04 &amp; 06.05. (Rodrigo) <strong>Deformation theory of associative algebras <\/strong>[Esp14, \u00a73.5\u20133.6], [Wal07, \u00a76.2], [CKTB05, \u00a73.1\u20133.5].<\/p>\n\n\n\n<p>13.05. (Christoph) <strong>Fedosov\u2019s construction I<\/strong> [Sch22, \u00a73.4], [Wal07, \u00a76.4], [Fed95, Ch. 3\u20135].<\/p>\n\n\n\n<p>20.05. (Ioan) <strong>Fedosov\u2019s construction II<\/strong> [Sch22, \u00a73.4], [Wal07, \u00a76.4], [Fed95, Ch. 3\u20135].<\/p>\n\n\n\n<p>27.05 (Ioan) <strong>Fedosov\u2019s construction III<\/strong> [Sch22, \u00a73.4], [Wal07, \u00a76.4], [Fed95, Ch. 3\u20135];<br>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(Jorn) <strong>Kontsevich\u2019s formality theorem I<\/strong> [Esp14, \u00a73.7\u20134.2], [CKTB05, Ch. 2], [Kon03], [CFT02].<\/p>\n\n\n\n<p>03.06. (Jorn) <strong>Kontsevich\u2019s formality theorem II<\/strong> [Esp14, \u00a73.7\u20134.2], [CKTB05, Ch. 2], [Kon03], [CFT02].<\/p>\n\n\n\n<p>10.06. <em>No seminar due to lecture-free week of Pentecost.<\/em><\/p>\n\n\n\n<p>17.06. <em>No seminar due to the \u201cCologne Representation Theory Day III\u201d.<\/em><\/p>\n\n\n\n<p>24.06. (Jorn) <strong>Kontsevich\u2019s formality theorem III<\/strong> [Esp14, \u00a73.7\u20134.2], [CKTB05, Ch. 2], [Kon03], [CFT02].<\/p>\n\n\n\n<p>01.07. <em>No seminar due to the \u201cInteractions of Poisson Geometry, Lie Theory and Symmetry\u201d conference in Lisbon.<\/em><\/p>\n\n\n\n<p>08.07. (Gustavo) <strong>The Lurie\u2013Pridham theorem<\/strong><\/p>\n\n\n\n<p>15.07. (Severin) <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[CFT02] Alberto Cattaneo, Giovanni Felder and Lorenzo Tomassini. \u2018From local to global deformation quantization of poisson manifolds\u2019. Duke Mathematical Journal,\n115(2), November 2002.\n\n    <\/p>\n    <p class=\"par-ind-spaced\">\n\n[CKTB05] Alberto Cattaneo, Bernhard Keller, Charles Torossian and Alain Bruguieres. \u2018D\u00e9formation, Quantification, Th\u00e9orie de Lie\u2019. Panoramas et Synthese, 2005.\n\n    <\/p>\n    <p class=\"par-ind-spaced\">\n\n[Esp14] Chiara Esposito. \u2018Formality Theory. From Poisson Structures to Deformation Quantization\u2019, volume 2 of SpringerBriefs in Mathematical Physics. Springer\nCham, 2014.\n\n    <\/p>\n    <p class=\"par-ind-spaced\">\n\n[Fed95] Boris Fedosov. \u2018Deformation Quantization and Index Theory\u2019. Wiley, 1995.\n\n    <\/p>\n    <p class=\"par-ind-spaced\">\n\n[Gut83] S. Gutt. \u2018An explicit *-product on the cotangent bundle of a Lie group\u2018. Letters in Mathematical Physics, 7:249\u2013258, 1983.\n\n    <\/p>\n    <p class=\"par-ind-spaced\">\n\n[Kon03] Maxim Kontsevich. \u2018Deformation Quantization of Poisson Manifolds\u2019. Letters in Mathematical Physics, 66:157\u2013216, 2003.\n\n    <\/p>\n    <p class=\"par-ind-spaced\">\n\n[MSS02] Martin Markl, Steve Shnider and Jim Stasheff. \u2018Operads in Algebra, Topology and Physics\u2019, volume 96 of Mathematical Surveys and Monographs. American Mathematical Society, 2002.\n\n    <\/p>\n    <p class=\"par-ind-spaced\">\n\n[Sch22] Jonas Schnitzer. \u2018Poisson Geometry and Deformation Quantization\u2019. <a href=\"https:\/\/home.mathematik.uni-freiburg.de\/geometrie\/lehre\/ws2022\/\nDQ\/pdf\/skript.pdf\">https:\/\/home.mathematik.uni-freiburg.de\/geometrie\/lehre\/ws2022\/\nDQ\/pdf\/skript.pdf<\/a>, 2022.\n\n    <\/p>\n    <p class=\"par-ind-spaced\">\n\n[Wal07] Stefan Waldmann. \u2018Poisson-Geometrie und Deformationsquantisierung. Eine Einf\u00fchrung\u2019. Springer Berlin, Heidelberg, 2007.\n\n    <\/p>\n<\/details>\n","protected":false},"excerpt":{"rendered":"<p>In the summer semester 2025, we will discuss deformation quantization in the Poisson geometry reading seminar. Formal deformation quantization is a mathematical framework that describes the transition from classical to quantum mechanics by deforming the algebra of functions on phase space. It replaces the classical pointwise product with a noncommutative star product parameterized by Planck\u2019s &hellip; <a href=\"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/learning-seminar\/ss-25\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;SS 25: Deformation Quantisation&#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-1687","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/pages\/1687","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=1687"}],"version-history":[{"count":32,"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/pages\/1687\/revisions"}],"predecessor-version":[{"id":2375,"href":"https:\/\/www.mi.uni-koeln.de\/PoissonGeometry\/wp-json\/wp\/v2\/pages\/1687\/revisions\/2375"}],"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=1687"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}