{"id":18,"date":"2021-06-24T01:42:33","date_gmt":"2021-06-24T01:42:33","guid":{"rendered":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/?page_id=18"},"modified":"2022-07-31T20:05:35","modified_gmt":"2022-07-31T20:05:35","slug":"schedule-2","status":"publish","type":"page","link":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/schedule-2\/","title":{"rendered":"Schedule and Content of the Lectures"},"content":{"rendered":"\n<ul class=\"wp-block-list\"><li>Day 1. <strong><mark style=\"background-color:#ffffff\" class=\"has-inline-color has-vivid-red-color\">Introduction to Homology and Persistent Homology<\/mark><\/strong><ul><li><strong>Lecture 1<\/strong>. Motivation and Basic Constructions \u2013 The shape of data, simplicial and cubical complexes, homology, persistent homology, persistence diagrams, Cech complexes, Vietoris-Rips complexes, digital images<\/li><li><strong>Lecture 2<\/strong>. Foundational Results \u2013 The persistence algorithm, Wasserstein distance, stability, flavors of persistence (e.g. zigzag, multiparameter)<\/li><\/ul><\/li><li>Day 2. <strong><mark style=\"background-color:#ffffff\" class=\"has-inline-color has-vivid-red-color\">Mathematics of Persistent Homology<\/mark><\/strong><ul><li><strong>Lecture 3<\/strong>. Algebra of Persistence Modules \u2013 Commutative algebra, representations of quivers, graded modules, algebraic stability<\/li><\/ul><ul><li><strong>Lecture 4<\/strong>. Geometry and Combinatorics \u2013 Geometric stability, M\u00f6bius inversion, coarse geometry<\/li><\/ul><\/li><li>Day 3. <strong><mark style=\"background-color:#ffffff\" class=\"has-inline-color has-vivid-red-color\">Statistics and Machine Learning<\/mark><\/strong><ul><li><strong>Lecture 5<\/strong>. Statistics \u2013 Hilbert spaces, kernels, persistence landscapes, averages, variance, hypothesis testing, permutation tests, principal component analysis, subsampling<\/li><li><strong>Lecture 6<\/strong>. Machine Learning \u2013 Classification, regression, support vector machines, deep learning, multilayer perceptrons, convolutional neural networks, topological loss, topological layers<\/li><\/ul><\/li><li>Day 4. <strong><mark style=\"background-color:#ffffff\" class=\"has-inline-color has-vivid-red-color\">Applications and Software<\/mark><\/strong><ul><li><strong>Lecture 7<\/strong>. Applications \u2013 Preprocessing, mathematical encoding of data, time series, case studies<\/li><li><strong>Lecture 8<\/strong>. Software and Algorithms \u2013 Computational advances, guide to current software<\/li><\/ul><\/li><li>Day 5. <strong><mark style=\"background-color:#ffffff\" class=\"has-inline-color has-vivid-red-color\">Advanced Topics and Current Research Problems<\/mark><\/strong><ul><li><strong>Lecture 9<\/strong>. Multiparameter Persistent Homology \u2013 Theory, algorithms, software, open problems<\/li><li><strong>Lecture 10<\/strong>. Mathematics of Persistent Homology \u2013 Graded persistence diagrams, virtual persistence diagrams, categorical stability, universal constructions, Cerf theory, open problems&#8221;<\/li><\/ul><\/li><\/ul>\n\n\n\n<p><em><em>All lectures take place in the STEAM Center, First Floor, Main Room<\/em> (Building 43 in the Campus Map, Address: 1302 N Patterson St, Valdosta, GA 31601)<br><em>Lab sessions take place in Odum Library, Room 3270<\/em> (Building 29 in the Campus Map)<\/em><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Preparation<\/h2>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-content\/uploads\/sites\/159\/2022\/07\/cbms_preparation-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Embed of Preparation..\"><\/object><a id=\"wp-block-file--media-42377076-0ff8-48a9-8557-b4c78428d341\" href=\"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-content\/uploads\/sites\/159\/2022\/07\/cbms_preparation-1.pdf\">Preparation<\/a><a href=\"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-content\/uploads\/sites\/159\/2022\/07\/cbms_preparation-1.pdf\" class=\"wp-block-file__button\" download aria-describedby=\"wp-block-file--media-42377076-0ff8-48a9-8557-b4c78428d341\">Download<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Day 1. Introduction to Homology and Persistent Homology Lecture 1. Motivation and Basic Constructions \u2013 The shape of data, simplicial and cubical complexes, homology, persistent homology, persistence diagrams, Cech complexes, Vietoris-Rips complexes, digital images Lecture 2. Foundational Results \u2013 The persistence algorithm, Wasserstein distance, stability, flavors of persistence (e.g. zigzag, multiparameter) Day 2. Mathematics of&hellip;<\/p>\n","protected":false},"author":457,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-18","page","type-page","status-publish","hentry","empty-entry-meta"],"acf":[],"_links":{"self":[{"href":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-json\/wp\/v2\/pages\/18","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-json\/wp\/v2\/users\/457"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-json\/wp\/v2\/comments?post=18"}],"version-history":[{"count":8,"href":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-json\/wp\/v2\/pages\/18\/revisions"}],"predecessor-version":[{"id":238,"href":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-json\/wp\/v2\/pages\/18\/revisions\/238"}],"wp:attachment":[{"href":"https:\/\/blog.valdosta.edu\/vsu-cbms-conference\/wp-json\/wp\/v2\/media?parent=18"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}