Guillaume Tahar

activity

20242026

collaborators

12 papers

math.GT2026

Bounds on saddle connections for flat spheres

Kai Fu, Guillaume Tahar

We consider a flat metric with conical singularities on the sphere. Under the assumption that no partial sum of angle defects is equal to $2 I ¨ $ , we draw on the geometry of immersed…

math.DG2026

Hybrid connections on Hessian manifolds

Arnaud ChÃ©ritat, Guillaume Tahar

A Hessian manifold $(M, D, g)$ is a manifold $M$ with a flat connection $D$ and a Riemannian or pseudo-Riemannian metric $g$ that is locally of the form $D^{2} f$ for some function $f$ …

math.GT2025

Isoperiodic foliation of the stratum $I^c ◯ M_{1} (1, 1, - 2)$

Gianluca Faraco, Guillaume Tahar, Yongquan Zhang

This paper describes the geometry and topology of leaves of the isoperiodic foliation of the stratum $I^c ◯ M_{1} (1, 1, - 2)$ . We prove that each leaf is a surface of infinite gen…

math.CV2025

The affine geometry of meromorphic connections with irregular singularities

Xavier Buff, Arnaud ChÃ©ritat, Guillaume Tahar

A meromorphic connection on the tangent bundle of a Riemann surface induces a complex affine structure on the complement of the poles. Local models for Fuchsian singularities are a…

math.DS2025

Conjugacies of geodesic flows in affine cylinders and tori

Xavier Buff, Guillaume Tahar

Affine cylinders (genus zero surfaces with two singularities) and affine tori (genus one surfaces without singularities) are among the simplest examples of surfaces endowed with a…

math.CV2025

K-differentials with prescribed singularities

Quentin Gendron, Guillaume Tahar

We study the local invariants that a meromorphic $k$ -differential on a Riemann surface of genus $g \geq 0$ can have for $k \geq 3$ . These local invariants include the orders of zer…