Speaker
Description
In this talk we discuss certain topological properties of the moduli space $\mathcal{MSph}_{g,n}(\vartheta)$ of spherical surfaces, namely surfaces of genus $g$ endowed with a metric of curvature $1$ with $n$ conical singularities of angles $2\pi\vartheta_1,...,2\pi\vartheta_n,$ and highlight how different they are from moduli spaces of surfaces of curvature $-1$. We show that their local structure can be studied through certain decorated representation spaces, which are also object of our investigation.
Concerning the global topological properties of $\mathcal{MSph}_{g,n}(\vartheta),$ we show that these moduli spaces are homotopy equivalent to finite cell complexes and that their connected components are non-compact (with very few exceptions). Time permitting, we will describe some explicit example.
This is joint work with Dmitri Panov (KCL).
