4 citations · 17 across the 18 of their papers we have counts for
27 papers
The affine geometry of meromorphic connections with irregular singularities
Xavier Buff, Arnaud Chéritat, 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…
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…
One-dimensional strata of residueless meromorphic differentials
Myeongjae Lee, Guillaume Tahar
In projectivized strata of meromorphic -forms on elliptic curves with only one zero, the locus of residueless differentials is a complex curve endowed with a canonical complex p…
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 , we draw on the geometry of immersed…
Isoperiodic foliation of the stratum
Gianluca Faraco, Guillaume Tahar, Yongquan Zhang
This paper describes the geometry and topology of leaves of the isoperiodic foliation of the stratum . We prove that each leaf is a surface of infinite genu…
Hybrid connections on Hessian manifolds
Arnaud Chéritat, Guillaume Tahar
We introduce a new class of affine connections on Hessian manifolds, called hybrid connections, characterized by the compatibility between their projective geometry with the underl…
Similarity surfaces, connections, and the measurable Riemann mapping theorem
Arnaud Chéritat, Guillaume Tahar
This article studies a particular process that approximates solutions of the Beltrami equation (straightening of ellipse fields, a.k.a. measurable Riemann mapping theorem) on $\mat…
K-differentials with prescribed singularities
Quentin Gendron, Guillaume Tahar
We study the local invariants that a meromorphic -differential on a Riemann surface of genus can have for . These local invariants include the orders of zer…
Linear first order differential operators and their Hutchinson-invariant sets
Per Alexandersson, Nils Hemmingsson, Dmitry Novikov +2
In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in details in the simplest case of…
Dihedral monodromy of cone spherical metrics
Quentin Gendron, Guillaume Tahar
Among metrics of constant positive curvature on a punctured compact Riemann surface with conical singularities at the punctures, dihedral monodromy means that the action of the mon…
Quadratic differentials with prescribed singularities
Quentin Gendron, Guillaume Tahar
The local invariants of a meromorphic quadratic differential on a compact Riemann surface are the orders of zeros and poles, and the residues at the poles of even orders. The main…
Closed geodesics in dilation surfaces
Adrien Boulanger, Selim Ghazouani, Guillaume Tahar
We prove that directions of closed geodesics in every dilation surface form a dense subset of the circle. The proof draws on a study of the degenerations of the Delaunay triangulat…
Horizon saddle connections and Morse-Smale dynamics of dilation surfaces
Guillaume Tahar
Dilation surfaces are generalizations of translation surfaces where the transition maps of the atlas are translations and homotheties with a positive ratio. In contrast with transl…
Abelian differentials with prescribed singularities
Quentin Gendron, Guillaume Tahar
The local invariants of a meromorphic Abelian differential on a Riemann surface of genus are the orders of zeros and poles, and the residues at the poles. The main result of th…
On limit sets for geodesics of meromorphic connections
Dmitry Novikov, Boris Shapiro, Guillaume Tahar
Meromorphic connections on Riemann surfaces originate and are closely related to the classical theory of linear ordinary differential equations with meromorphic coefficients. Limit…
Isoresidual fibration and resonance arrangements
Quentin Gendron, Guillaume Tahar
The stratum of meromorphic -forms with a zero of order and poles of orders on the Riemann sphere has a map, the isor…
Geometric decompositions of surfaces with spherical metric and conical singularities
Guillaume Tahar
We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic a…
On existence of quasi-Strebel structures for meromorphic k-differentials
Boris Shapiro, Guillaume Tahar
In this paper, motivated by the classical notion of a Strebel quadratic differential on a compact Riemann surfaces without boundary we introduce the notion of a quasi-Strebel struc…
Triangulations of branched affine surfaces
Guillaume Tahar
A branched affine structure on a compact topological surface with marked points is a complex affine structure outside the marked points. We give a proof of an unpublished foundatio…
A topological bound on the Cantor-Bendixson rank of meromorphic differentials
Guillaume Tahar
In translation surfaces of finite area (corresponding to holomorphic differentials), directions of saddle connections are dense in the unit circle. On the contrary, saddle connecti…
Horizon saddle connections, quasi-Hopf surfaces and Veech groups of dilation surfaces
Guillaume Tahar
Dilation surfaces are generalizations of translation surfaces where the geometric structure is modelled on the complex plane up to affine maps whose linear part is real. They are t…
Chamber structure of modular curves
Guillaume Tahar
Modular curves parametrize elliptic curves with a point of order . They can be identified with connected components of projectivized strata $\mathbb{P}\mathcal{H}(a,-…
Ordered algebraic structures and classification of semifields
Guillaume Tahar
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type…
Geometric triangulations and flips
Guillaume Tahar
We prove that for a given flat surface with conical singularities, any pair of geometric triangulations can be connected by a chain of flips.