The APDE seminar on Monday, 11\/25 will be given by Charles Hadfield in Evans 939 from 4:10 to 5pm. <\/p>\n\n\n\n
Title: Dynamical zeta functions at zero on surfaces with boundary<\/p>\n\n\n\n
Abstract: The Ruelle zeta function counts closed geodesics on a Riemannian manifold of negative curvature. Its zeroes are related to Pollicott-Ruelle resonances which have been heavily studied in the setting of Anosov dynamical systems. In 2016, Dyatlov-Zworski proved an unexpected result relating the structure of the zeta function near the origin to the topology of the manifold. This extended a formula previously only known to hold in the constant curvature setting.<\/p>\n\n\n\n
This talk will consider the situation where the manifold has boundary. A similar story can be told and the ultimate result extends the constant curvature setting (understood in 2001) to the variable curvature setting.<\/p>\n\n\n\n
The microlocal tools required to consider this problem had been well developed in earlier papers (principally Dyatlov-Guillarmou 2016) and it remained to manipulate correctly relative cohomology (in this case \u00e0 la Bott-Tu) in order to understand the space of 1-form Pollicott-Ruelle resonances.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"
The APDE seminar on Monday, 11\/25 will be given by Charles Hadfield in Evans 939 from 4:10 to 5pm. Title: Dynamical zeta functions at zero on surfaces with boundary Abstract: The Ruelle zeta function counts closed geodesics on a Riemannian manifold of negative curvature. Its zeroes are related to Pollicott-Ruelle resonances which have been heavily […]<\/p>\n","protected":false},"author":104,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-777","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/777","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/104"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=777"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/777\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}