Mario Garcia-Fernandez (ICMAT, Madrid) will speak in the geometry seminar on Tuesday 24 March 2020 at 11ham in the Salle des Profs. Mario’s title is *Gravitating vortices with positive curvature* and his abstract is below.

*I will overview recent work with Chengjian Yao and Vamsi Pingali in arXiv:1911.09616, where we give a complete solution to the existence problem for gravitating vortices with positive topological constant c>0, as introduced in arXiv:1510.03810. Our main result establishes the existence of solutions provided that a GIT stability condition for an effective divisor on the Riemann sphere is satisfied. To this end, we use a continuity path starting from Yang’s solution with c=0, and deform the coupling constant α towards 0. A salient feature of our argument is a new bound S(g) \geq c for the curvature of gravitating vortices, which we apply to construct a limiting solution along the path via Cheeger-Gromov theory. *