Conférencier: Mario Garcia-Fernandez, ICMAT, Madrid

Résumé / Abstract: In this talk I will overview recent joint work with Vamsi  Pingali and Chengjian Yao in arXiv:1911.09616 about gravitating  vortices. These equations couple a Kähler metric on a compact  Riemann surface with a hermitian metric over a holomorphic line bundle  equipped with a fixed global section --- the Higgs field ---, and have  a symplectic interpretation as moment-map equations.In our work we give a complete solution to the existence problem for gravitating vortices on the Riemann sphere with positive topological constant c > 0. Our main result establishes the existence of solutions provided that a GIT stability condition for an effective divisor on CP^1 is satisfied. To this end, we use a continuity path starting from Yang's solution with c = 0. A salient feature of our argument is a new bound S \geq c for the curvature of gravitating vortices, which we apply to construct a limiting solution along the path via Cheeger-Gromov theory.

Le lien pour se connecter est : https://uqam.zoom.us/j/98999725241