{"id":523,"date":"2022-06-21T09:41:49","date_gmt":"2022-06-21T13:41:49","guid":{"rendered":"https:\/\/blogarchive.utc.edu\/campus-weekly\/?p=523"},"modified":"2022-06-21T09:43:01","modified_gmt":"2022-06-21T13:43:01","slug":"special-colloquium-lecture-series-part-1","status":"publish","type":"post","link":"https:\/\/blogarchive.utc.edu\/campus-weekly\/2022\/06\/special-colloquium-lecture-series-part-1\/","title":{"rendered":"Special Colloquium Lecture Series, Part 1"},"content":{"rendered":"\n<p>Dear Colleagues,<\/p>\n\n\n\n<p>This summer, the Department of Mathematics is running an online Special Colloquium Lecture Series on mathematical analysis and applications in allied fields. This lecture series is presented in conjunction with UTC\u2019s NSF-funded <a href=\"https:\/\/sites.google.com\/mocs.utc.edu\/nsfutcreusite\/home\">Math REU Site<\/a>. The first lecture will be given next Monday, June 27th by Dr. Chris Marx, Associate Professor of Mathematics at Oberlin College and Conservatory. I have included the details of Dr. Marx\u2019s lecture below. Undergraduate and graduate students who are interested in Analysis, Partial Differential Equations, and Mathematical Physics are especially encouraged to attend.<\/p>\n\n\n\n<p>Sincerely,<\/p>\n\n\n\n<p>Roger Nichols<\/p>\n\n\n\n<p><strong>Speaker:<\/strong> <a href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Fwww.oberlin.edu%2Fchris-marx&amp;sa=D&amp;sntz=1&amp;usg=AOvVaw16yiidJu77pSabHAoZs9dG\" target=\"_blank\" rel=\"noreferrer noopener\">Dr. Chris Marx<\/a> (<a href=\"https:\/\/www.google.com\/url?q=https%3A%2F%2Fwww.oberlin.edu&amp;sa=D&amp;sntz=1&amp;usg=AOvVaw0zlPXffp2ZnjqAuRbJ8nAp\" target=\"_blank\" rel=\"noreferrer noopener\">Oberlin College and Conservatory<\/a>)<\/p>\n\n\n\n<p><strong>Date:<\/strong> Monday, June 27, 2022<\/p>\n\n\n\n<p><strong>Time:<\/strong> 2:00 p.m.-3:00 p.m. (EDT)<\/p>\n\n\n\n<p><strong>Zoom link:<\/strong> <a href=\"https:\/\/tennessee.zoom.us\/j\/94587985368\">https:\/\/tennessee.zoom.us\/j\/94587985368<\/a><\/p>\n\n\n\n<p><strong>Zoom password:<\/strong> 591806<\/p>\n\n\n\n<p><strong>Title:<\/strong> Agmon-type Decay of Eigenfunctions for a Class of Schr\u00f6dinger Operators with Non-compact Classically Allowed Region<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> An important result by Agmon implies that an eigenfunction of a Schr\u00f6dinger operator in $\\mathbb{R}^d$ with an eigenvalue below the bottom of the essential spectrum decays exponentially if the associated classically allowed region is compact.<\/p>\n\n\n\n<p>We extend this result to a class of Schr\u00f6dinger operators with eigenvalues, for which the classically allowed region is not necessarily compactly supported: We show that integrability of the characteristic function of the classically allowed region with respect to an increasing weight function of bounded logarithmic derivative leads to $L^2$-decay of the eigenfunction with respect to the same weight.<\/p>\n\n\n\n<p>Here, the decay is measured in the Agmon metric, which takes into account anisotropies of the potential. In particular, for a power law (or, respectively, exponential) weight, our main result implies that power law (or, respectively, exponential) decay of &#8220;the size of the classically allowed region&#8221; allows to conclude power law (or, respectively, exponential) decay, in the Agmon metric, of the eigenfunction.<\/p>\n\n\n\n<p>The work presented in this talk is the result of joint research with my recent honors student, Hengrui Zhu (Oberlin \u201921).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dear Colleagues, This summer, the Department of Mathematics is running an online Special Colloquium Lecture Series on mathematical analysis and applications in allied fields. This lecture series is presented in conjunction with UTC\u2019s NSF-funded Math REU Site. The first lecture will be given next Monday, June 27th by Dr. Chris Marx, Associate Professor of Mathematics&hellip; <\/p>\n<p class=\"more-link-wrap\"><span><a class=\"more-link button text\" href=\"https:\/\/blogarchive.utc.edu\/campus-weekly\/2022\/06\/special-colloquium-lecture-series-part-1\/\"><span>Continue Reading <\/span><\/a><\/span><\/p>\n","protected":false},"author":1493,"featured_media":22,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[15,120183,8,120186],"tags":[],"class_list":{"0":"post-523","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-campus","8":"category-faculty-staff","9":"category-news","10":"category-students-news","11":"entry"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Special Colloquium Lecture Series, Part 1 - Campus Updates Archive<\/title>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Special Colloquium Lecture Series, Part 1 - Campus Updates Archive\" \/>\n<meta property=\"og:description\" content=\"Dear Colleagues, This summer, the Department of Mathematics is running an online Special Colloquium Lecture Series on mathematical analysis and applications in allied fields. 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