Abstract

Meromorphic 1-forms on the Riemann sphere with prescribed orders of singularities form strataendowed with period coordinates. Fixing residues at the poles defines a fibration of any stratum tothe vector space of configurations of residues. in a joint work with Quentin Gendron, it has beenproved that for strata of 1-forms with only one zero, the isoresidual fibration is a cover of the spaceof configurations of residues ramified over an arrangement of complex hyperplanes called theresonance arrangement. Using combinatorics of decorated tree and the dictionary betweencomplex analysis and flat geometry, we give a formula to compute the degree of this cover andinvestigate its monodromy. in a more recent work with Dawei Chen, Quentin Gendron and MiauePrado, we investigate the case of strata with two zeroes where isoresidual fibers are complexcurves endowed with a canonical translation structure. Singularities of this structure providetopological invariants of the fibers that refine the Euler characteristic and still lack an interpretationin terms of enumerative geometry.

Speaker Intro

Guillaume Tahar is a BlMSA assistant professor. Before joining BlMSA he held a seniorpostdoctoral fellowship in Weizmann Institute of Science. He contributedto the study of modulispaces of various flavours of geometric structures on surfaces: translation and dilation structuresflat metrics and cone spherical metrics. His recent research interests of include linear differentiaoperators, isoresidual fibrations and simplicial arrangements of lines.