Gianluca Faraco

activity

20172026

most citedTranslation surfaces and periods of meromorphic differentials

6 citations · 16 across the 17 of their papers we have counts for

collaborators

18 papers

math.GT2026

The dark side of translation surfaces: It is not all about dynamics

Gianluca Faraco

This survey offers a geometric and topological perspective on translation surfaces, with a focus on aspects that are often overshadowed by the dynamical viewpoint. After presenting…

math.GT2025

On the symplectic geometry of branched hyperbolic surfaces in genus two

Gianluca Faraco, Arnaud Maret

We construct analogues of Fenchel-Nielsen coordinates on an open and dense subset of the space of holonomies of branched hyperbolic structures on a closed genus-2 surface. We show…

math.GT2025

Relative period realization of holomorphic differentials with prescribed invariants

Dawei Chen, Gianluca Faraco

We provide a complete description of realizable relative period representations for holomorphic differentials on Riemann surfaces with prescribed orders of zeros and additional inv…

math.DS2024

Mapping class group orbit closures for Deroin-Tholozan representations

Yohann Bouilly, Gianluca Faraco, Arnaud Maret

We prove that infinite mapping class group orbits are dense in the character variety of Deroin-Tholozan representations. In other words, the action is minimal except for finite orb…

math.GT2023

Simple loop conjecture for discrete representations in PSL $(2, R)$

Gianluca Faraco, Subhojoy Gupta

We show that the Simple Loop Conjecture holds for any representation $ρ : π_{1} (S) ⟶ PSL (2, R)$ that is discrete but not faithful. That is, we show th…

math.GT2023

Isoperiodic foliation of the stratum $Ω M_{1} (1, 1, - 2)$

Gianluca Faraco, Guillaume Tahar, Yongquan Zhang

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

math.GT2023

Counterexamples to the simple loop conjecture in higher-dimension

Gianluca Faraco

For every $g \geq 2$ and $n \geq 4$ , we provide an $n -$ manifold $M$ and a continuous $2 -$ sided map $f : S ⟶ M$ , where $S$ is a closed genus $g$ surface, such that no si…

math.HO2023★ 1 cited

Tessellations of surfaces

Gianluca Faraco

A tessellation or tiling is a collection of sets, called tiles, that cover a plane without gaps and overlaps. The present note is an invitation to get to know the beauty and majest…

math.GT2022★ 2 cited

Period realization of meromorphic differentials with prescribed invariants

Dawei Chen, Gianluca Faraco

We provide a complete description of realizable period representations for meromorphic differentials on Riemann surfaces with prescribed orders of zeros and poles, hyperelliptic st…

math.DS2022★ 1 cited

On the distality and expansivity of certain maps on spheres

Manoj Choudhuri, Gianluca Faraco, Alok Kumar Yadav

Any affine map on the (n+1)-dimensional Euclidean space gives rise to a natural map on the n-dimensional sphere whose dynamical aspects are not so well-studied in the literature. W…

math.GT2022

On the automorphism groups of certain branched structures on surfaces

Gianluca Faraco

We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct…

math.GT2021★ 2 cited

Monodromy of Schwarzian equations with regular singularities

Gianluca Faraco, Subhojoy Gupta

Let $S$ be a punctured surface of finite type and negative Euler characteristic. We determine all possible representations $ρ : π_{1} (S) \to PSL_{2} (C)$ that arise as the…

math.DS2021

Modular orbits on the representation spaces of compact abelian Lie groups

Yohann Bouilly, Gianluca Faraco

Let $S$ be a closed surface of genus $g$ greater than zero. In the present paper we study the topological-dynamical action of the mapping class group on the $T^{n}$ -character va…

math.GT2021★ 6 cited

Translation surfaces and periods of meromorphic differentials

Shabarish Chenakkod, Gianluca Faraco, Subhojoy Gupta

Let $S$ be an oriented surface of genus $g$ and $n$ punctures. The periods of any meromorphic differential on $S$ , with respect to a choice of complex structure, determine a repres…

math.CV2018

Distances on the moduli space of complex projective structures

Gianluca Faraco

Let $S$ be a closed and oriented surface of genus $g$ at least $2$ . In this (mostly expository) article, the object of study is the space $P (S)$ of marked isomorphism cla…

math.GT2018

Geometrization of almost extremal representations in $PSL_{2} R$

Gianluca Faraco

Let $S$ be a closed surface of genus $g$ . In this paper, we investigate the relationship between hyperbolic cone-structure on $S$ and representations of the fundamental group into…

math.GT2017

Geometrization of purely hyperbolic representations in $PSL_{2} R$

Gianluca Faraco

Let $S$ be a surface of genus $g$ at least $2$ . A representation $ρ : π_{1} S ⟶ PSL_{2} R$ is said to be purely hyperbolic if its image consists only of hyperbolic…

math.GT2017★ 4 cited

Complex projective structures with maximal number of Möbius transformations

Gianluca Faraco, Lorenzo Ruffoni

We consider complex projective structures on Riemann surfaces and their groups of projective automorphisms. We show that the structures achieving the maximal possible number of pro…

The dark side of translation surfaces: It is not all about dynamics

On the symplectic geometry of branched hyperbolic surfaces in genus two

Relative period realization of holomorphic differentials with prescribed invariants

Mapping class group orbit closures for Deroin-Tholozan representations

Simple loop conjecture for discrete representations in PSL(2,R)

Isoperiodic foliation of the stratum ΩM1​(1,1,−2)

Counterexamples to the simple loop conjecture in higher-dimension

Tessellations of surfaces

Period realization of meromorphic differentials with prescribed invariants

On the distality and expansivity of certain maps on spheres

On the automorphism groups of certain branched structures on surfaces

Monodromy of Schwarzian equations with regular singularities

Modular orbits on the representation spaces of compact abelian Lie groups

Translation surfaces and periods of meromorphic differentials

Distances on the moduli space of complex projective structures

Geometrization of almost extremal representations in PSL2​R

Geometrization of purely hyperbolic representations in PSL2​R

Complex projective structures with maximal number of Möbius transformations

Simple loop conjecture for discrete representations in PSL $(2, R)$

Isoperiodic foliation of the stratum $Ω M_{1} (1, 1, - 2)$

Geometrization of almost extremal representations in $PSL_{2} R$

Geometrization of purely hyperbolic representations in $PSL_{2} R$