{"id":1499,"date":"2025-11-24T10:21:49","date_gmt":"2025-11-24T18:21:49","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1499"},"modified":"2025-11-29T19:48:45","modified_gmt":"2025-11-30T03:48:45","slug":"effective-non-linear-pdes-from-statistical-many-body-dynamics","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2025\/11\/24\/effective-non-linear-pdes-from-statistical-many-body-dynamics\/","title":{"rendered":"Effective non-linear PDEs from statistical many-body dynamics"},"content":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0<b>November 25th<\/b>, will be at\u00a0<strong>3:30pm<\/strong>\u00a0in\u00a0<strong>Room 740<\/strong>.<\/p>\n<p><strong>Speaker:\u00a0<\/strong>Joe Miller<\/p>\n<p><strong>Abstract:<\/strong> Interacting systems of particles and waves are foundational in many natural phenomena. This talk will outline mathematical approaches for deriving effective, statistical descriptions of such many-body dynamics by connecting them to solutions of nonlinear partial differential equations. Key examples include (i) the Boltzmann equation, which emerges as a limit of interacting hard spheres, (ii) the nonlinear Schr\u00f6dinger equation, which describes quantum particle dynamics initialized near a Bose-Einstein condensate, (iii) the Vlasov equation, which is an effective model for both non-collisional particles evolving under Newtonian dynamics or as a semiclassical limit of fermionic interactions, and (iv) the kinetic wave equations, which model the statistical behavior of interacting waves. I will discuss my joint work on each of these equations, highlighting how to frame these PDEs as limits of the underlying particle or wave dynamics. Time permitting, I will discuss ongoing work on deriving a Boltzmann mean field game from a jump diffusion process.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0November 25th, will be at\u00a03:30pm\u00a0in\u00a0Room 740. Speaker:\u00a0Joe Miller Abstract: Interacting systems of particles and waves are foundational in many natural phenomena. This talk will outline mathematical approaches for deriving effective, statistical descriptions of such many-body dynamics by connecting them to solutions of nonlinear partial differential equations. Key examples include (i) the [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25,1],"tags":[],"class_list":["post-1499","post","type-post","status-publish","format-standard","hentry","category-fall-2025","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1499","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\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1499"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1499\/revisions"}],"predecessor-version":[{"id":1500,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1499\/revisions\/1500"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1499"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1499"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1499"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}