{"id":1274,"date":"2024-01-14T19:45:43","date_gmt":"2024-01-14T18:45:43","guid":{"rendered":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/?p=1274"},"modified":"2024-02-17T21:15:16","modified_gmt":"2024-02-17T20:15:16","slug":"phd-course-foliations","status":"publish","type":"post","link":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/2024\/01\/14\/phd-course-foliations\/","title":{"rendered":"PhD Course: Foliations"},"content":{"rendered":"

Foliations<\/span><\/h1>\n

Prof. Gianluca Bande<\/b>
\nDipartimento di Matematica e Informatica
\nUniversit\u00e0 degli Studi di Cagliari<\/span><\/p>\n

Abstract<\/b><\/span><\/p>\n

The course is an introduction to the Theory of Foliations. Basic knowledge of Differential Geometry is required and the basics of Fundamental Group.<\/span><\/span><\/p>\n

Outline<\/b><\/span><\/p>\n

– Definition(s) and examples of Foliations. Dynamical systems. Frobenius\u2019 Theorem.
\n<\/span>– Holonomy of a leaf and the Reeb Stability Theorem. Basic and foliated Cohomology. Godbillion-Vey class for a codimension 1 foliation on a 3-manifold.
\n– The Reeb foliation: definition and a 3D-printer model. Novikov and Likorisch Theorem.<\/span><\/span><\/p>\n

Schedule<\/b><\/span><\/p>\n

The course spans over 3 lectures of 2 hours each (6 hours total). The lectures will be given on February 5, February 12, February 15 \u2013 2024 at 4:30 p.m. in Room B of the Department of Mathematics and Computer Science.<\/span><\/span><\/p>\n

Exam<\/b><\/span><\/p>\n

The final exam consists in a presentation.<\/span><\/span><\/p>\n

References<\/b><\/span><\/p>\n

1. C. <\/span>Camacho and A. Lins Neto, <\/span>Geometric theory of foliations<\/span><\/strong>, Birkh\u00e4user, 1985.
\n2. <\/span>A. Candel;\u00a0L. <\/span>Conlon, <\/span>Foliations I<\/span><\/strong>, Grad. Stud. Math.\u00a023, American Mathematical Society,\u00a0Providence, 2000.
\n3. <\/span>P. Tondeur, <\/span>Geometry of Foliations<\/span><\/strong>, Monogr. Math 90, <\/span>Birkh\u00e4user Verlag,\u00a0Basel<\/span>,<\/em>\u00a01997.<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Foliations Prof. Gianluca Bande Dipartimento di Matematica e Informatica Universit\u00e0 degli Studi di Cagliari Abstract The course is an introduction to the Theory of Foliations. Basic knowledge of Differential Geometry is required and the basics of […]<\/p>\n","protected":false},"author":244,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,10],"tags":[],"class_list":["post-1274","post","type-post","status-publish","format-standard","hentry","category-dipartimento-matematica-informatica","category-events"],"_links":{"self":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1274","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/users\/244"}],"replies":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/comments?post=1274"}],"version-history":[{"count":5,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1274\/revisions"}],"predecessor-version":[{"id":1299,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1274\/revisions\/1299"}],"wp:attachment":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/media?parent=1274"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/categories?post=1274"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/tags?post=1274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}