{"id":15647,"date":"2022-07-27T19:01:23","date_gmt":"2022-07-27T10:01:23","guid":{"rendered":"https:\/\/www.waseda.jp\/fsci\/mathphys\/?p=15647"},"modified":"2023-12-05T12:16:57","modified_gmt":"2023-12-05T03:16:57","slug":"%e7%89%b9%e5%88%a5%e8%ac%9b%e7%be%a9%e3%80%8c%e3%83%a9%e3%83%b3%e3%83%80%e3%83%a0%e5%aa%92%e8%b3%aa%e4%b8%ad%e3%81%ae%e7%a2%ba%e7%8e%87%e9%81%8e%e7%a8%8b%e3%80%8d%e9%96%8b%e5%82%ac","status":"publish","type":"post","link":"https:\/\/www.waseda.jp\/fsci\/mathphys\/news\/15647","title":{"rendered":"\u7279\u5225\u8b1b\u7fa9\u300c\u30e9\u30f3\u30c0\u30e0\u5a92\u8cea\u4e2d\u306e\u78ba\u7387\u904e\u7a0b\u300d\u958b\u50ac"},"content":{"rendered":"<p>\u6570\u7269\u7cfb\u79d1\u5b66\u62e0\u70b9\u3067\u306f\u30012022\u5e7410\u670810\u65e5\uff08\u6708\uff09\u306817\u65e5\uff08\u6708\uff09\u306b\u3001\u56fd\u969b\u6559\u80b2\u6d3b\u52d5\u306e\u4e00\u74b0\u3068\u3057\u3066\u6a19\u8a18\u7279\u5225\u8b1b\u7fa9\u3092\u958b\u50ac\u3057\u307e\u3059\u3002Martin T. Barlow\u5148\u751f\u3068\u798f\u5cf6\u7adc\u8f1d\u5148\u751f\u3092\u8b1b\u6f14\u8005\u306b\u304a\u8fce\u3048\u3057\u3001\u6570\u7406\u7269\u7406\u5b66\u306b\u52d5\u6a5f\u4ed8\u3051\u3092\u6301\u3064\u30e9\u30f3\u30c0\u30e0\u5a92\u8cea\u4e2d\u306e\u78ba\u7387\u904e\u7a0b\u306b\u3064\u3044\u3066\u3001\u57fa\u790e\u7684\u306a\u90e8\u5206\u304b\u3089\u6700\u65b0\u306e\u7814\u7a76\u6210\u679c\u306b\u81f3\u308b\u307e\u3067\u3054\u8b1b\u6f14\u3044\u305f\u3060\u304f\u4e88\u5b9a\u3067\u3059\u3002<\/p>\n<h3>\u8b1b\u7fa9\u30bf\u30a4\u30c8\u30eb<\/h3>\n<p>\u300e\u30e9\u30f3\u30c0\u30e0\u5a92\u8cea\u4e2d\u306e\u78ba\u7387\u904e\u7a0b\uff08Stochastic Processes in Random media\uff09\u300f \u7279\u5225\u8b1b\u7fa9<\/p>\n<h3>\u65e5\u7a0b<\/h3>\n<h5 class=\"moz-quote-pre\">2022\u5e7410\u670810\u65e5\uff08\u6708\uff09<\/h5>\n<ul>\n<li>14:30-16:10\u3000\u798f\u5cf6\u7adc\u8f1d\uff08\u7b51\u6ce2\u5927\u5b66\u3000\u6570\u7406\u7269\u8cea\u7cfb \u51c6\u6559\u6388\uff09<\/li>\n<li>16:30-18:30\u3000Martin T. Barlow\uff08University of British Columbia: Emeritus Professor\uff09<\/li>\n<\/ul>\n<h5>2022\u5e7410\u670817\u65e5\uff08\u6708\uff09<\/h5>\n<ul>\n<li>14:30-16:10\u3000\u798f\u5cf6\u7adc\u8f1d\uff08\u7b51\u6ce2\u5927\u5b66\u3000\u6570\u7406\u7269\u8cea\u7cfb \u51c6\u6559\u6388\uff09<\/li>\n<li>16:30-18:30\u3000Martin T. Barlow\uff08University of British Columbia: Emeritus Professor\uff09<\/li>\n<\/ul>\n<h3>\u8b1b\u5e2b<\/h3>\n<div class=\"table-wrapper\"><table border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 201px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15701 size-thumbnail\" src=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2022\/07\/MBarlow-S-270x270.jpg\" alt=\"\" width=\"270\" height=\"270\" \/><\/td>\n<td style=\"width: 682px;\">\n<h6><strong><a href=\"https:\/\/personal.math.ubc.ca\/~barlow\/\" target=\"_blank\" rel=\"noopener\">Martin T. Barlow\u5148\u751f<\/a><\/strong><\/h6>\n<p>University of British Columbia: Emeritus Professor<\/p>\n<p>\u8b1b\u6f14\u30bf\u30a4\u30c8\u30eb\uff1aHarnack inequalities: from PDE to graphs, fractals and metric spaces<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 201px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-15703 size-thumbnail\" src=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2022\/07\/Fukushima-S-270x270.jpg\" alt=\"\" width=\"270\" height=\"270\" \/><\/td>\n<td style=\"width: 682px;\">\n<h6><a href=\"https:\/\/nc.math.tsukuba.ac.jp\/column\/Ryoki_Fukushima\" target=\"_blank\" rel=\"noopener\">\u798f\u5cf6\u7adc\u8f1d\u5148\u751f<\/a><\/h6>\n<p>\u7b51\u6ce2\u5927\u5b66 \u6570\u7406\u7269\u8cea\u7cfb \u51c6\u6559\u6388<\/p>\n<p>\u8b1b\u6f14\u30bf\u30a4\u30c8\u30eb\uff1aProbabilistic aspects of the Anderson model<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<h3>\u4f1a\u5834<\/h3>\n<p><a href=\"https:\/\/www.waseda.jp\/top\/access\/nishiwaseda-campus\" target=\"_blank\" rel=\"noopener\">\u65e9\u7a32\u7530\u5927\u5b66\u897f\u65e9\u7a32\u7530\u30ad\u30e3\u30f3\u30d1\u30b9<\/a>\u300063\u53f7\u99282\u968e05\u4f1a\u8b70\u5ba4\uff0fZoom\u306b\u3088\u308b\u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u958b\u50ac\u4e88\u5b9a<\/p>\n<h3>\u8a00\u8a9e<\/h3>\n<p>\u82f1\u8a9e<\/p>\n<h3>\u5bfe\u8c61<\/h3>\n<p>\u7814\u7a76\u8005\u3001\u5b66\u751f<\/p>\n<h3>\u4e8b\u524d\u767b\u9332<\/h3>\n<p>\u4e8b\u524d\u767b\u9332\u304c\u5fc5\u8981\u3067\u3059\u3002\u53c2\u52a0\u3092\u5e0c\u671b\u3055\u308c\u308b\u65b9\u306f\u3001<a href=\"https:\/\/forms.gle\/Q4qTMXDjHuubcDFy7\" target=\"_blank\" rel=\"noopener\">\u3053\u3061\u3089<\/a>\u304b\u3089\u53c2\u52a0\u767b\u9332\u3092\u304a\u9858\u3044\u3057\u307e\u3059\u3002<\/p>\n<h3>\u304a\u554f\u5408\u305b<\/h3>\n<h6>\u3010\u8b1b\u7fa9\u5185\u5bb9\u7b49\u306b\u95a2\u3059\u308b\u304a\u554f\u5408\u308f\u305b\u3011<\/h6>\n<p>\u65e9\u7a32\u7530\u5927\u5b66\u57fa\u5e79\u7406\u5de5\u5b66\u90e8\u6570\u5b66\u79d1\u3000\u718a\u8c37\u9686 \u6559\u6388\u3000t-kumagai\uff3bat\uff3dwaseda.jp<\/p>\n<h6>\u3010\u53c2\u52a0\u767b\u9332\u7b49\u306b\u95a2\u3059\u308b\u304a\u554f\u5408\u305b\u3011<\/h6>\n<p>SGU\u6570\u7269\u7cfb\u79d1\u5b66\u62e0\u70b9\u3000info [at] sgu-mathphys.sci.waseda.ac.jp<\/p>\n<h3>\u30bf\u30a4\u30e0\u30c6\u30fc\u30d6\u30eb\u3000\u203b\u8cea\u7591\u5fdc\u7b54\u6642\u9593\u3092\u542b\u3080<\/h3>\n<h4>10\u670810\u65e5\uff08\u6708\uff09<\/h4>\n<div class=\"table-wrapper\"><table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 13.964%;\">\n<h6>14:30 &#8211; 16:10<\/h6>\n<\/td>\n<td style=\"width: 86.036%;\">\n<h5>\u798f\u5cf6\u7adc\u8f1d \u51c6\u6559\u6388\uff08\u7b51\u6ce2\u5927\u5b66\u3000\u6570\u7406\u7269\u8cea\u7cfb\uff09<br \/>\n&#8220;Anderson localization, Lifshiz tail and a polymer model&#8221;<\/h5>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 13.964%;\"><\/td>\n<td style=\"width: 86.036%;\">\uff08\u8b1b\u7fa9\u6982\u8981\uff09<br \/>\nThe Anderson Hamiltonian is a Schroedinger operator with random potential. The random potential is usually assumed to be stationary and ergodic, which roughly means that it is macroscopically homogeneous. However, its spectral properties exhibit striking differences to the case of periodic potentials: there are dense pure point spectrum with localized eigenfunctions around the ground state energy. In the first half of this lecture, I will quickly review some of the results in this direction. In the second half, I will focus on a part of the proof where a probabilistic method called &#8220;large deviation principle&#8221; plays an important role. There we also encounter a seemingly unrelated polymer model which is of interest itself.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 13.964%;\">\n<h6>16:30 &#8211; 18:30<\/h6>\n<\/td>\n<td style=\"width: 86.036%;\">\n<h5>Martin T. Barlow \u6559\u6388\uff08University of British Columbia\uff09<br \/>\n&#8220;Harnack inequalities: from PDE to graphs, fractals and metric spaces (1)&#8221;<\/h5>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 13.964%;\"><\/td>\n<td style=\"width: 86.036%;\">\uff08\u8b1b\u7fa9\u6982\u8981\uff09<br \/>\nA major problem in PDE, solved independently in the late 1950s by de Giorgi, Moser and Nash,\u00a0 was the regularity of solutions to second order divergence form equations. Moser&#8217;s approach was to prove a Harnack inequality, which can be understood in probabilistic terms. The Harnack inequalities (elliptic and parabolic) of Moser are versatile and powerful tools: for example they imply immediately the Liouville property &#8212; ie that all bounded harmonic functions are constant.<br \/>\nThe proof techniques of de Giorgi, Moser and Nash are also very robust, and can be adapted to graphs and general metric spaces. These lectures will focus on the stability of these Harnack inequalities under perturbations of the space, such as by rough isometries.<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<p>&nbsp;<\/p>\n<h4>10\u670817\u65e5\uff08\u6708\uff09<\/h4>\n<div class=\"table-wrapper\"><table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr style=\"height: 24px;\">\n<td style=\"width: 13.964%; height: 24px;\">\n<h6>14:30 &#8211; 16:10<\/h6>\n<\/td>\n<td style=\"width: 86.036%; height: 24px;\">\n<h5>\u798f\u5cf6\u7adc\u8f1d \u51c6\u6559\u6388\uff08\u7b51\u6ce2\u5927\u5b66\u3000\u6570\u7406\u7269\u8cea\u7cfb\uff09<br \/>\n&#8220;Quenched localization for the parabolic Anderson model&#8221;<\/h5>\n<\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 13.964%; height: 24px;\"><\/td>\n<td style=\"width: 86.036%; height: 24px;\">\uff08\u8b1b\u7fa9\u6982\u8981\uff09<br \/>\nThe Anderson Hamiltonian was introduced to describe the motion of an electron in a disordered material, but it can also be used to describe the behavior of the heat with random sources and sinks by considering the corresponding parabolic problem. This direction has also been studied actively since 1990 and rather complete results have been proved for various models. In the first half of this lecture, I will mainly discuss the case of unbounded potentials, where the so-called<br \/>\nthe extreme value theory plays an important role. In the second half, I will explain more recent advances in the case of bounded potentials.<\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 13.964%; height: 24px;\">\n<h6>16:30 &#8211; 18:30<\/h6>\n<\/td>\n<td style=\"width: 86.036%; height: 24px;\">\n<h5>Martin T. Barlow \u6559\u6388\uff08University of British Columbia\uff09<br \/>\n&#8220;Harnack inequalities: from PDE to graphs, fractals and metric spaces (2)&#8221;<\/h5>\n<\/td>\n<\/tr>\n<tr style=\"height: 24px;\">\n<td style=\"width: 13.964%; height: 24px;\"><\/td>\n<td style=\"width: 86.036%; height: 24px;\">\uff08\u8b1b\u7fa9\u6982\u8981\uff09<br \/>\nA major problem in PDE, solved independently in the late 1950s by de Giorgi, Moser and Nash,\u00a0 was the regularity of solutions to second order divergence form equations. Moser&#8217;s approach was to prove a Harnack inequality, which can be understood in probabilistic terms. The Harnack inequalities (elliptic and parabolic) of Moser are versatile and powerful tools: for example they imply immediately the Liouville property &#8212; ie that all bounded harmonic functions are constant.<br \/>\nThe proof techniques of de Giorgi, Moser and Nash are also very robust, and can be adapted to graphs and general metric spaces. These lectures will focus on the stability of these Harnack inequalities under perturbations of the space, such as by rough isometries.<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<p>&nbsp;<\/p>\n<ul>\n<li><a href=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2022\/07\/Poster20221010-17.pdf\" target=\"_blank\" rel=\"noopener\">\u30dd\u30b9\u30bf\u30fc<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u7269\u7cfb\u79d1\u5b66\u62e0\u70b9\u3067\u306f\u30012022\u5e7410\u670810\u65e5\uff08\u6708\uff09\u306817\u65e5\uff08\u6708\uff09\u306b\u3001\u56fd\u969b\u6559\u80b2\u6d3b\u52d5\u306e\u4e00\u74b0\u3068\u3057\u3066\u6a19\u8a18\u7279\u5225\u8b1b\u7fa9\u3092\u958b\u50ac\u3057\u307e\u3059\u3002Martin T. Barlow\u5148\u751f\u3068\u798f\u5cf6\u7adc\u8f1d\u5148\u751f\u3092\u8b1b\u6f14\u8005\u306b\u304a\u8fce\u3048\u3057\u3001\u6570\u7406\u7269\u7406\u5b66\u306b\u52d5\u6a5f\u4ed8\u3051\u3092\u6301\u3064\u30e9\u30f3\u30c0\u30e0 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":15688,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[53,139,162],"class_list":["post-15647","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news","tag-events","tag-lecture","tag-education"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts\/15647","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/comments?post=15647"}],"version-history":[{"count":2,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts\/15647\/revisions"}],"predecessor-version":[{"id":18415,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts\/15647\/revisions\/18415"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/media\/15688"}],"wp:attachment":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/media?parent=15647"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/categories?post=15647"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/tags?post=15647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}