Date(s) - 02/10/2018
11 h 00 min - 12 h 00 min
In this talk we discuss two types of problems related to spherical (i.e. K=1) surfaces with conical singularities and their moduli spaces: problems of the first type concern the moduli space itself, problems of the second type concern the locus of spherical metrics in a fixed conformal class. Among questions of the first type, we focus on (non-)emptiness and (dis)connectedness of the moduli space. Among questions of the second type, we prove an inequality between spherical systole and conformal systole that allow us to show that loci of metrics in a conformal class are compact and to analyze what happens if some conical angle is very small.
This is joint work with Dmitri Panov.