4 citations · 17 across the 18 of their papers we have counts for
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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…
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…
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…
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…
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 We give a proof of an unpublished foundatio…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…
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.
Veech groups of flat surfaces with poles
Guillaume Tahar
Flat surfaces that correspond to meromorphic -forms or to meromorphic quadratic differentials containing poles of order two and higher are surfaces of infinite area. We classify…
Counting saddle connections in flat surfaces with poles of higher order
Guillaume Tahar
Flat surfaces that correspond to -differentials on compact Riemann surfaces are of finite area provided there is no pole of order or higher. We denote by \textit{flat surfac…
On the number of saddle connections in translation surfaces with poles
Guillaume Tahar
Translation surfaces with poles correspond to meromorphic differentials on compact Riemann surfaces. They appear in compactifications of strata of the moduli space of Abelian diffe…