{"id":50977,"date":"2026-07-30T09:46:45","date_gmt":"2026-07-30T07:46:45","guid":{"rendered":"https:\/\/www.h-its.org\/de\/event\/hits-colloquium-michael-baake-the-markov-embedding-problem-old-and-new\/"},"modified":"2026-07-30T09:59:10","modified_gmt":"2026-07-30T07:59:10","slug":"hits-colloquium-michael-baake-the-markov-embedding-problem-old-and-new","status":"publish","type":"tribe_events","link":"https:\/\/www.h-its.org\/de\/event\/hits-colloquium-michael-baake-the-markov-embedding-problem-old-and-new\/","title":{"rendered":"HITS Colloquium Michael Baake &#8211; The Markov embedding problem &#8211; old and new"},"content":{"rendered":"<p>&nbsp;<\/p>\n<p>by <a href=\"https:\/\/www.math.uni-bielefeld.de\/baake\/\">Michael Baake<\/a>, Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld<\/p>\n<p>&nbsp;<\/p>\n<p>Markov matrices are a widely used tool for the empirical description<br \/>\nof real-world data, which are usually sampled in discrete time steps.<br \/>\nSince the underlying processes may (and often do) run in continuous<br \/>\ntime, one needs some time interpolation consistency, as the Finnish<br \/>\nstatistician Gustav Elfving realised almost a century ago. This led to<br \/>\nthe embedding question as an important research problem, where one<br \/>\nneeds to know whether a given Markov matrix possesses a real matrix<br \/>\nlogarithm that is a Markov generator (or rate matrix).<\/p>\n<p>After initial contributions by David G. Kendall and Sir John F. C.<br \/>\nKingman in the early 1960s, the embedding problem was finally solved<br \/>\nfor three-dimensional matrices by the mid 1990s, after which further<br \/>\nactivities faded. This changed again when molecular evolution and<br \/>\nbioinformatics needed the classification in four dimensions, which was<br \/>\nachieved just a few years ago. The field has been active ever since.<\/p>\n<p>Here, we give an introduction to the problem and present some key<br \/>\nresults, both old and new. The embedding of Markov matrices is a good<br \/>\nexample of a problem that emerged from the applications, but requires<br \/>\na blend of mathematical tools from different directions, including<br \/>\nprobability theory, matrix analysis and abstract algebra.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>REGISTRATION:<\/strong><\/p>\n<p>The talk will be hybrid.<\/p>\n<p>If you would like to participate online, please register in advance <a href=\"https:\/\/kta-email.zoom.us\/meeting\/register\/E8URVYJBT_C5UZFH3WrT7w\">here<\/a>.<\/p>\n<p>After registering, you will receive a confirmation email containing information about joining the meeting.<\/p>\n<p>In case you are not able to attend, you can watch the talk afterwards on the HITS YouTube channel:\u00a0<a href=\"https:\/\/www.youtube.com\/user\/TheHITSters\">https:\/\/www.youtube.com\/user\/TheHITSters<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; by Michael Baake, Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld &nbsp; Markov matrices are a widely used tool for &#8230;<\/p>\n","protected":false},"author":168,"featured_media":29944,"template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"_tribe_events_status":"","_tribe_events_status_reason":"","footnotes":""},"tags":[],"hits-research-group":[],"tribe_events_cat":[1408,1345],"class_list":["post-50977","tribe_events","type-tribe_events","status-publish","has-post-thumbnail","hentry","tribe_events_cat-kolloquien","tribe_events_cat-oeffentliche-veranstaltungen","cat_kolloquien","cat_oeffentliche-veranstaltungen"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>HITS Colloquium Michael Baake - The Markov embedding problem - old and new - HITS gGmbH<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.h-its.org\/de\/event\/hits-colloquium-michael-baake-the-markov-embedding-problem-old-and-new\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"HITS Colloquium Michael Baake - The Markov embedding problem - old and new - HITS gGmbH\" \/>\n<meta property=\"og:description\" content=\"&nbsp; 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