### On some properties of spherical surfaces with conical singularities and their moduli spaces

Ergodic Theory and Dynamical Systems Seminar

3rd May 2018, 3:00 pm – 4:00 pm

Howard House, 4th Floor Seminar Room

Spherical surfaces are 2-dimensional (connected, oriented) manifolds endowed with a Riemannian metric of curvature 1. By Gauss-Bonnet theorem the only compact example is the round sphere. On the other hand, there are plenty of examples if one allows conical singularities, and indeed such surfaces can be described by real-analytic moduli spaces. In this talk we first discuss when such moduli spaces are non-empty and we show that there are cases in which they can have many connected components. Moreover, we explain how metric and conformal invariants on such surfaces are related and we draw some conclusion about the non-existence of metrics in a fixed conformal class with one small angle.

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