Seminar

The study of spherical metrics with conical singularities have seen a lot of recent development and yet there are still a lot of open problems. We will focus on a special class called spherical conical metrics with reducible monodromy. Each of such metrics is canonically associated with a meromorphic one-form, and there is also a connection with translation surfaces. This talk will focus on the recent work, joint with Bin Xu, on the spectral properties of such metrics. We obtain a spectral characterization of the monodromy property, which establishes a new connection between the geometric microlocal analysis which is about the study of singular operators, and the classical complex analysis approach that uses the developing maps.