{"id":1314,"date":"2025-04-24T10:42:53","date_gmt":"2025-04-24T17:42:53","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1314"},"modified":"2025-05-04T19:35:32","modified_gmt":"2025-05-05T02:35:32","slug":"what-are-chern-numbers-and-why-do-they-matter-in-condensed-matter-physics","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/04\/24\/what-are-chern-numbers-and-why-do-they-matter-in-condensed-matter-physics\/","title":{"rendered":"What are Chern numbers and why do they matter in condensed matter physics?"},"content":{"rendered":"<div class=\"entry-content\">\n<p>The HADES seminar on Tuesday, <strong>April 29th<\/strong>, will be at\u00a0<strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:<\/strong> Maciej Zworski<\/p>\n<p><strong>Abstract:\u00a0<\/strong>Chern numbers are analytically constructed topological invariants of complex line bundles over surfaces and a special case of Chern classes. I will introduce this concept in a simple case of the Bloch sphere and show how related objects such as the Berry curvature (introduced by Barry Simon) appear in the adiabatic theorem (which I will state and explain). I will then move to tori and the line bundle of Bloch eigenfunctions. Its topology will then be related to decay of eigenfunctions as discussed in many physics and maths papers including the recent paper by Simon Becker, Zhongkai Tao and Mengxuan Yang (with some of the authors present to answer any hard questions).<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday, April 29th, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker: Maciej Zworski Abstract:\u00a0Chern numbers are analytically constructed topological invariants of complex line bundles over surfaces and a special case of Chern classes. I will introduce this concept in a simple case of the Bloch sphere and show how related objects such as the [&hellip;]<\/p>\n","protected":false},"author":92,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[],"class_list":["post-1314","post","type-post","status-publish","format-standard","hentry","category-spring-2025"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1314","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/92"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1314"}],"version-history":[{"count":3,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1314\/revisions"}],"predecessor-version":[{"id":1318,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1314\/revisions\/1318"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1314"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1314"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1314"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}