{"id":1823,"date":"2015-06-25T15:51:09","date_gmt":"2015-06-25T13:51:09","guid":{"rendered":"http:\/\/www.mi.uni-koeln.de\/opt\/?page_id=1823"},"modified":"2015-10-16T13:08:20","modified_gmt":"2015-10-16T11:08:20","slug":"bms-summer-school","status":"publish","type":"page","link":"http:\/\/www.mi.uni-koeln.de\/opt\/veranstaltungen\/bms-summer-school\/","title":{"rendered":"BMS Summer School: Packings, Coverings, and Embeddings"},"content":{"rendered":"

Lecturer<\/strong>
\nProf. Dr. Frank Vallentin<\/a><\/p>\n

Teaching assistants<\/strong>
\nM.Sc. Maria Dostert<\/a>, M.Sc. Jan Rolfes<\/a><\/p>\n

Summary<\/strong>
\nIt will be shown how to use semidefinite optimization in discrete geometry. Covered topics will include: Finding upper bounds for geometric packing problems, constructing optimal lattice sphere coverings, and computing low-distortion embeddings of finite metric spaces into Euclidean spaces.<\/p>\n

Problem Sheets<\/strong>
\nSheet 1: Conic optimization<\/a>
\nSheet 2: Embeddings<\/a>
\nSheet 3: Coverings<\/a>
\nSheet 4: Packings<\/a><\/p>\n

Software<\/strong>
\nB. Borchers – CSDP Solver<\/a>
\nA. Garber, A. Sch\u00fcrmann, F. Vallentin – scc (secondary cone cruiser)<\/a><\/p>\n

Literature<\/strong>
\nGeneral:<\/em>
\nM. Laurent, F. Vallentin – Semidefinite Optimization, 2012<\/a>
\nConic optimization:<\/em>
\nA. Nemirovski – Advances in convex optimization: conic programming, 2007<\/a>
\nD. de Laat – A ten page introduction to conic optimization, 2015<\/a>
\nEmbeddings:<\/em>
\nS. Hoory, N. Linial, A. Wigderson – Expander graphs and their applications, 2006<\/a>
\nJ. Matousek – Lectures on Discrete Geometry (Chapter 15), 2005<\/a>
\n F. Vallentin – Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces, 2008<\/a>
\nCoverings:<\/em>
\nA. Sch\u00fcrmann, F. Vallentin – Computational Approaches to Lattice Packing and Covering Problems, 2006<\/a>
\nM. Dutour-Sikiric, A. Sch\u00fcrmann, F. Vallentin – A generalization of Voronoi’s reduction theory and its application, 2008<\/a>
\nM. Dutour-Sikiric, A. Sch\u00fcrmann, F. Vallentin – Inhomogeneous extreme forms, 2012<\/a>
\nPackings:<\/em>
\nP.E.B. DeCorte, D. de Laat, F. Vallentin – Fourier analysis on finite groups and the Lov\u00e1sz theta-number of Cayley graphs, 2014<\/a>
\nF.M. de Oliveira Filho, F. Vallentin – Mathematical optimization for packing problems, 2014<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Lecturer Prof. Dr. Frank Vallentin Teaching assistants M.Sc. Maria Dostert, M.Sc. Jan Rolfes Summary It will be shown how to use semidefinite optimization in discrete geometry. Covered topics will include: Finding upper bounds for geometric packing problems, constructing optimal lattice sphere coverings, and computing low-distortion embeddings of finite metric spaces into Euclidean spaces. Problem Sheets … „BMS Summer School: Packings, Coverings, and Embeddings“ <\/span>weiterlesen<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"parent":25,"menu_order":25,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1823","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages\/1823","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/comments?post=1823"}],"version-history":[{"count":18,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages\/1823\/revisions"}],"predecessor-version":[{"id":6176,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages\/1823\/revisions\/6176"}],"up":[{"embeddable":true,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages\/25"}],"wp:attachment":[{"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/media?parent=1823"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}