On the topology of isoresidual fibers
Organizer
Speaker
Time
Thursday, March 13, 2025 1:30 PM - 2:30 PM
Venue
A3-2a-201
Abstract
Meromorphic 1-forms on the Riemann sphere, with prescribed orders of singularities, form strata equipped with period coordinates. Fixing the residues at the poles defines the isoresidual fibration of any given stratum onto the vector space of residue configurations.
In a joint work with Dawei Chen, Quentin Gendron and Miguel Prado, we show that for strata with two zeroes, isoresidual fibers are complex curves endowed with a canonical translation structure. The singularities of these fibers encode, through their local invariants, the corresponding degenerations of the parametrized objects in the multi-scale boundary. In particular, computing the genus of the underlying complex curve is reduced to a purely combinatorial problem.
As an application, we provide the classification of connected components of generic isoresidual fibers for strata with an arbitrary number of zeroes.
Speaker Intro
Guillaume Tahar obtained his Ph.D from Université Paris Diderot, under the supervision of Anton Zorich. He was a senior postdoctoral fellow in Weizmann Institute of Science and joined BIMSA as an assistant professor in 2022. He contributed to the study of moduli spaces of various flavours of geometric structures on surfaces. His results include proving the existence of closed geodesics in dilation surfaces and the complete characterization of configurations of local invariants realized by a differential on a Riemann surface. His recent research interests include linear differential operators, simplicial arrangements of lines and quantum invariants of knots.