{"id":1252,"date":"2014-04-07T13:33:29","date_gmt":"2014-04-07T13:33:29","guid":{"rendered":"http:\/\/blogs.truman.edu\/mathcs\/?p=1252"},"modified":"2014-04-07T13:33:29","modified_gmt":"2014-04-07T13:33:29","slug":"colloquium-talk","status":"publish","type":"post","link":"https:\/\/blogs.truman.edu\/mathcs\/2014\/04\/07\/colloquium-talk\/","title":{"rendered":"Colloquium Talk"},"content":{"rendered":"<p><strong>Kevin Gerstle<\/strong> from the University of Iowa<\/p>\n<p><strong>Brownian Motion and HMD-Functions<\/strong><\/p>\n<p>3:30pm, Wednesday\u00a0(4\/9\/2014)<br \/>\nVH1224<\/p>\n<p>Models of random motion can be used in all scientific disciplines to<br \/>\nstudy phenomena ranging from the rise and fall of stock prices to the<br \/>\nmotion of pollen particles through water. In particular, models of<br \/>\nBrownian motion can be used to describe the behavior of random,<br \/>\ncontinuous motion through any number of dimensions.<br \/>\nBy letting these randomly moving particles, ie: Brownian particles,<br \/>\ntravel through a two-dimensional domain, we can learn valuable<br \/>\ninformation about the shape and structure of the domain by determining<br \/>\nhow far from their starting points Brownian particles will first hit the<br \/>\ndomain&#8217;s boundary. In doing so, we will construct the &#8220;harmonic measure<br \/>\ndistribution functions&#8221; (HMD-functions) for these domains and discuss<br \/>\njust what information these functions encode. For example: are the<br \/>\ndomains bounded? Do they have any corners or cusps? Do they have any<br \/>\nholes in them? Are their boundaries connected?<br \/>\nWe will examine the HMD-functions of several different types of domains<br \/>\nusing both geometrical and computational methods and then look in<br \/>\nparticular at a class of circle domains for which the HMD-functions are<br \/>\nof particular interest. In doing so, we will use concepts from analysis,<br \/>\ngeometry, probability, and computational theory in order to define these<br \/>\nfunctions and to explain their significance.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kevin Gerstle from the University of Iowa Brownian Motion and HMD-Functions 3:30pm, Wednesday\u00a0(4\/9\/2014) VH1224 Models of random motion can be used in all scientific disciplines to study phenomena ranging from the rise and fall of stock prices to the motion of pollen particles through water. In particular, models of Brownian motion can be used to [&hellip;]<\/p>\n","protected":false},"author":213,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1178],"tags":[],"class_list":["post-1252","post","type-post","status-publish","format-standard","hentry","category-events"],"acf":[],"_links":{"self":[{"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/posts\/1252","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/users\/213"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/comments?post=1252"}],"version-history":[{"count":1,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/posts\/1252\/revisions"}],"predecessor-version":[{"id":1253,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/posts\/1252\/revisions\/1253"}],"wp:attachment":[{"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/media?parent=1252"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/categories?post=1252"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/tags?post=1252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}