{"id":881,"date":"2020-10-26T01:58:13","date_gmt":"2020-10-26T08:58:13","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=881"},"modified":"2020-10-26T01:58:13","modified_gmt":"2020-10-26T08:58:13","slug":"jared-speck-vanderbilt","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2020\/10\/26\/jared-speck-vanderbilt\/","title":{"rendered":"Jared Speck (Vanderbilt)"},"content":{"rendered":"\n\t\t\t\t\n<p>The  APDE seminar on Monday, 11\/09, will be given by Jared Speck online via Zoom from <strong>4:10 to 5:00pm<\/strong>.  To participate, email Georgios Moschidis (gmoschidis@berkeley.edu) or Federico Pasqualotto (fpasqualotto@berkeley.edu).   <\/p>\n\n\n\n<p>Title:  Stable Big Bang formation in general relativity: The complete sub-critical regime.<\/p>\n\n\n\n<p>Abstract:  The celebrated theorems of Hawking and Penrose show that under appropriate assumptions on the matter model, a large, open set of initial data for Einstein\u2019s equations lead to geodesically incomplete solutions. However, these theorems are \u201csoft\u201d in that they do not yield any information about the nature of the incompleteness, leaving open the possibilities that i) it is tied to the blowup of some invariant quantity (such as curvature) or ii) it is due to a more sinister phenomenon, such as incompleteness due to lack of information for how to uniquely continue the solution (this is roughly known as the formation of a Cauchy horizon). Despite the \u201cgeneral ambiguity,\u201d in the mathematical physics literature, there are heuristic results, going back 50 years, suggesting that whenever a certain \u201csub-criticality\u201d condition holds, the Hawking\u2013Penrose incompleteness is caused by the formation of a Big Bang singularity, that is, curvature blowup along an entire spacelike hypersurface. In recent joint work with I. Rodnianski and G. Fournodavlos, we have given a rigorous proof of the heuristics. More precisely, our results apply to Sobolev-class perturbations \u2013 without symmetry  \u2013 of generalized Kasner solutions whose exponents satisfy the sub-criticality condition. Our main theorem shows that \u2013 like the generalized Kasner solutions \u2013 the perturbed solutions develop Big Bang singularities. In this talk, I will provide an overview of our result and explain how it is tied to some of the main themes of investigation by the mathematical general relativity community, including the remarkable work of Dafermos\u2013Luk on the stability of Kerr Cauchy horizons. I will also discuss the new gauge that we used in our work, as well as intriguing connections to other problems concerning stable singularity formation.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 11\/09, will be given by Jared Speck online via Zoom from 4:10 to 5:00pm. To participate, email Georgios Moschidis (gmoschidis@berkeley.edu) or Federico Pasqualotto (fpasqualotto@berkeley.edu). Title: Stable Big Bang formation in general relativity: The complete sub-critical regime. Abstract: The celebrated theorems of Hawking and Penrose show that under appropriate assumptions on [&hellip;]<\/p>\n","protected":false},"author":109,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-881","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/881","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\/109"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=881"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/881\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=881"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=881"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=881"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}