BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mario Garcia-Fernandez (ICMAT\, Madrid) DTSTART:20210115T160000Z DTEND:20210115T171500Z DTSTAMP:20260423T005653Z UID:CIRGET/27 DESCRIPTION:Title: Gravitating vortices with positive curvature\nby Mario Garcia-Fernande z (ICMAT\, Madrid) as part of CRM - Séminaire du CIRGET / Géométrie et Topologie\n\n\nAbstract\nIn this talk I will overview recent joint work wi th Vamsi \nPingali and Chengjian Yao in arXiv:1911.09616 about gravitating \nvortices. These equations couple a K\\"ahler metric on a compact \nRiem ann surface with a hermitian metric over a holomorphic line bundle \nequip ped with a fixed global section --- the Higgs field ---\, and have \na sym plectic interpretation as moment-map equations.\n\nIn our work we give a c omplete solution to the existence problem for \ngravitating vortices on th e Riemann sphere with positive topological \nconstant c > 0. Our main resu lt establishes the existence of solutions \nprovided that a GIT stability condition for an effective divisor on \nCP^1 is satisfied. To this end\, w e use a continuity path starting from \nYang's solution with c = 0. A sali ent feature of our argument is a new \nbound S \\geq c for the curvature o f gravitating\nvortices\, which we apply to construct a limiting solution along the \npath via Cheeger-Gromov theory.\n LOCATION:https://researchseminars.org/talk/CIRGET/27/ END:VEVENT END:VCALENDAR