Title: Quadratic differentials and applications to spherical geometry (joint work with Quentin Gendron)
Speaker: Guillaume Tahar (Weizmann Institute)
Date: 09 February 2022
Time: 4 pm
Venue: Microsoft Teams (online)
Up to biholomorphic change of variable, local invariants of a quadratic differential at some point of a Riemann surface are the order and the residue if the point is a pole of even order. Using the geometric interpretation in terms of flat surfaces, we solve the Riemann-Hilbert type problem of characterizing the sets of local invariants that can be realized by a pair (X,q) where X is a compact Riemann surface and q is a meromorphic quadratic differential.
As an application to geometry of surfaces with positive curvature, we give a complete characterization of the distributions of conical angles that can be realized by a cone spherical metric with dihedral monodromy.