Differential Geometry Seminar: Moduli spaces of spherical surfaces with conical singularities

Seminar | May 6 | 3:10-4 p.m. | 939 Evans Hall

 Dmitri Panov, University College London

 Department of Mathematics

A spherical surface with $n$ conical singularities is a surface $S$ with cone points $x_1, \dots ,x_n$ and a metric $g$, such that $g$ has curvature 1 on the complement $S \setminus (x_1,...,x_n)$ and has a conical singularity of angle $2\pi (\theta _i)$ at each $x_i$. Moduli spaces of spherical metrics with fixed angles are intriguing objects. Up to very recently the most basic questions about these spaces were open, in particular it was not known for which angles such spaces are non-empty, whether they can be disconnected, whether they project surjectively to the moduli space of curves with $n$ marked points. I'll speak about solutions of such questions, the talk is based on a joint work with Gabirele Mondello.