BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Da Rong Cheng (University of Miami) DTSTART:20250527T140000Z DTEND:20250527T150000Z DTSTAMP:20260423T022717Z UID:Geolis/170 DESCRIPTION:Title: SU(2) Yang-Mills-Higgs functional with self-interaction term on 3-manifol ds\nby Da Rong Cheng (University of Miami) as part of Geometria em Lis boa (IST)\n\n\nAbstract\nI will talk about recent joint work with Daniel F adel (University of São Paulo) and Luiz Lara (Unicamp)\, where we study t he SU(2) Yang-Mills-Higgs functional with positive coupling constant on 3- manifolds. Motivated by the work of Alessandro Pigati and Daniel Stern (20 21) on the U(1)-version of the functional\, we also include a scaling para meter.\n\nWhen the 3-manifold is closed and the parameter is small enough\ , by adapting to our context the min-max method used by Pigati and Stern\, we construct non-trivial critical points satisfying energy upper and lowe r bounds that are natural from the point of view of scaling.\n\nThen\, ove r 3-manifolds with bounded geometry\, we show that\, in the limit as the p arameter tends to zero\, and under the above-mentioned energy upper bound\ , a sequence of critical points exhibits concentration phenomenon at a fin ite collection of points\, while the remaining energy goes into an $L^2$ h armonic 1-form. Moreover\, the concentrated energy at each point is accoun ted for by finitely many "bubbles"\, that is\, non-trivial critical points on $R^3$ with the scaling parameter set to 1.\n LOCATION:https://researchseminars.org/talk/Geolis/170/ END:VEVENT END:VCALENDAR