{"id":456,"date":"2022-02-07T09:22:20","date_gmt":"2022-02-07T17:22:20","guid":{"rendered":"\/wp\/hades\/?p=456"},"modified":"2022-02-07T09:22:20","modified_gmt":"2022-02-07T17:22:20","slug":"almost-sure-weyl-law-for-toeplitz-operators","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2022\/02\/07\/almost-sure-weyl-law-for-toeplitz-operators\/","title":{"rendered":"Almost Sure Weyl Law for Toeplitz Operators"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,&nbsp;<strong>February 8<\/strong> will be at <strong>3:30 pm<\/strong> in <strong>Room 740<\/strong>.<\/p>\n\n\n\n<p><strong>Speaker<\/strong>: Izak Oltman<\/p>\n\n\n\n<p><strong>Abstract<\/strong>: When computing eigenvalues of finite-rank non-self-adjoint operators, significant numerical inaccuracies often occur when the rank of the operator is sufficiently large. I show the spectrum of Toeplitz operators, with a random perturbation added, satisfy a Weyl law with probability close to one. I will begin with numerical animations, demonstrating this result for quantizations of the torus (a result proven by Martin Vogel in 2020). Then give a brief introduction to Toeplitz operator (quantizations of functions on Kahler Manifolds). And finally outline the main parts of the proof, which involve constructing an `exotic calculus\u2019 of symbols on a Kahler manifold.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,&nbsp;February 8 will be at 3:30 pm in Room 740. Speaker: Izak Oltman Abstract: When computing eigenvalues of finite-rank non-self-adjoint operators, significant numerical inaccuracies often occur when the rank of the operator is sufficiently large. I show the spectrum of Toeplitz operators, with a random perturbation added, satisfy a Weyl law [&hellip;]<\/p>\n","protected":false},"author":91,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-456","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/456","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\/91"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=456"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/456\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=456"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=456"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=456"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}