{"id":1056,"date":"2022-04-12T14:34:28","date_gmt":"2022-04-12T21:34:28","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/apde\/?p=1056"},"modified":"2022-04-12T14:34:28","modified_gmt":"2022-04-12T21:34:28","slug":"tadahiro-oh-university-of-edinburgh","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2022\/04\/12\/tadahiro-oh-university-of-edinburgh\/","title":{"rendered":"Tadahiro Oh (University of Edinburgh)"},"content":{"rendered":"\n\t\t\t\t\n<p>The APDE seminar on Monday, 4\/18, will be given by Tadahiro Oh (University of Edinburgh) online via Zoom from <strong>4:10pm to 5:00pm PST<\/strong>. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu).<\/p>\n\n\n\n<p><strong>Title<\/strong>: Gibbs measures, canonical stochastic quantization,<br>and singular stochastic wave equations<\/p>\n\n\n\n<p><strong>Abstract<\/strong>:<br>In this talk, I will discuss the (non-)construction of the focusing<br>Gibbs measures and the associated dynamical problems. This study was<br>initiated by Lebowitz, Rose, and Speer (1988) and continued by Bourgain<br>(1994), Brydges-Slade (1996), and Carlen-Fr\u00f6hlich-Lebowitz (2016). In<br>the one-dimensional setting, we consider the mass-critical case, where a<br>critical mass threshold is given by the mass of the ground state on the<br>real line. In this case, I will show that the Gibbs measure is indeed<br>normalizable at the optimal mass threshold, thus answering an open<br>question posed by Lebowitz, Rose, and Speer (1988).<\/p>\n\n\n\n<p>In the three dimensional-setting, I will first discuss the construction<br>of the $\\Phi^3_3$-measure with a cubic interaction potential. This<br>problem turns out to be critical, exhibiting a phase transition:<br>normalizability in the weakly nonlinear regime and non-normalizability<br>in the strongly nonlinear regime. Then, I will discuss the dynamical<br>problem for the canonical stochastic quantization of the<br>$\\Phi^3_3$-measure, namely, the three-dimensional stochastic damped<br>nonlinear wave equation with a quadratic nonlinearity forced by an<br>additive space-time white noise (= the hyperbolic $\\Phi^3_3$-model). As<br>for the local theory, I will describe the paracontrolled approach to<br>study stochastic nonlinear wave equations, introduced in my work with<br>Gubinelli and Koch (2018). In the globalization part, I introduce a new,<br>conceptually simple and straightforward approach, where we directly work<br>with the (truncated) Gibbs measure, using the variational formula and<br>ideas from theory of optimal transport.<\/p>\n\n\n\n<p>The first part of the talk is based on a joint work with Philippe Sosoe<br>(Cornell) and Leonardo Tolomeo (Bonn), while the second part is based on<br>a joint work with Mamoru Okamoto (Osaka) and Leonardo Tolomeo (Bonn).<br><\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The APDE seminar on Monday, 4\/18, will be given by Tadahiro Oh (University of Edinburgh) online via Zoom from 4:10pm to 5:00pm PST. To participate, email Sung-Jin Oh (sjoh@math.berkeley.edu). Title: Gibbs measures, canonical stochastic quantization,and singular stochastic wave equations Abstract:In this talk, I will discuss the (non-)construction of the focusingGibbs measures and the associated dynamical [&hellip;]<\/p>\n","protected":false},"author":106,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1056","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1056","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\/106"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=1056"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/1056\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=1056"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=1056"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=1056"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}