Mathematical Sciences Research Institute

Home » Workshop » Schedules » Integrability meets Control Theory: Harmonic Maps in General Relativity

Integrability meets Control Theory: Harmonic Maps in General Relativity

Connections for Women: Mathematical General Relativity September 03, 2013 - September 04, 2013

September 04, 2013 (09:00 AM PDT - 10:00 AM PDT)
Speaker(s): Shabnam Beheshti (Rutgers University)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Abstract We provide a framework for analyzing axially symmetric harmonic maps on R3 with symmetric target spaces G=K. Drawing on results from analysis to Lie theory to geometry, we give a complete and rigorous proof that, all such maps are completely integrable. We further demonstrate that new solutions to the harmonic map equations can be generated from a given seed solution, using a dressing or vesture method. This uni es the integrability of theories including chiral eld models, nonlinear -models, Yang-Mills and Einstein electrovacuum equations in the general context of harmonic maps. Utility of the vesture method is made concrete by generating N-solitonic harmonic maps into a noncompact Grassmann manifold G = SU(p; q). We demonstrate a special case by deriving Kerr and Kerr-Newman solutions from the Minkowski initial seed for the Einstein vacuum and Einstein- Maxwell cases, respectively. In performing an asymptotic analysis, these solutions are shown to be in the hyperextreme sector of the corresponding parameters, suggesting constraints on the dressing mechanism. We indicate the possibility of using this analysis to control the resulting N-black hole confi gurations in this setting.
17463?type=thumb Beheshti_Abtract 43.9 KB application/pdf Download
18951?type=thumb Beheshti 217 KB application/pdf Download
Video/Audio Files


H.264 Video v1156.m4v 345 MB video/mp4 rtsp://videos.msri.org/data/000/017/703/original/v1156.m4v Download
Quicktime v1156.mov 499 MB video/quicktime rtsp://videos.msri.org/data/000/017/704/original/v1156.mov Download
Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture. The videos are sold at cost for $20USD (shipping included). Please Click Here to send an email to MSRI to purchase the DVD.

See more of our Streaming videos on our main VMath - Streaming Video page.