7 nov 2019 -- 16:00   [open in google calendar]

Aula Magna, Dipartimento di Matematica, Università di Pisa

Abstract.

The study of solutions of Liouville's equation with prescribed logarithmic singularities is the same as the study of constant curvature metrics on a Riemann surface with prescribed conic points. Understanding such metrics is a classic problem that remains a very active area. I will survey some of the substantial literature on this and then describe a series of papers with Xuwen Zhu which attempts to understand this problem via deformation theory when the cone angles are large. This involves finding a new geometric framework in which the methods of global analysis can be applied.