Irene Pasquinelli

• Research Associate at University of Bristol

We classify representations of a class of Deligne-Mostow lattices into PGL(3,C). In particular, we show local rigidity for the representations (of Deligne-Mostow lattices with three-fold symmetry and of type one) where the generators we chose are of the same type as the generators of Deligne-Mostow lattices. We also show local rigidity without cons...

We complete the classification of type preserving representations of Deligne-Mostow lattices with 3-fold symmetry into PGL(3,C) started in arXiv:2003.06466. In particular, we show local rigidity for all the representations where the generators we chose are of the same type as the generators of the Deligne-Mostow lattices. We use formal computations...

Let $S$ be a connected non-orientable surface with negative Euler characteristic and of finite type. We describe the possible closures in $\mathcal M\mathcal L$ and $\mathcal P\mathcal M\mathcal L$ of the mapping class group orbits of measured laminations, projective measured laminations and points in Teichm\"uller space. In particular we obtain a...

We classify representations of a class of Deligne-Mostow lattices into PGL(3;C). In particular, we show local rigidity for the representations (of Deligne-Mostow lattices with 3-fold symmetry and of type one) where the generators we chose are of the same type as the generators of Deligne-Mostow lattices. We also show local rigidity without constrai...

A class of complex hyperbolic lattices in PU(2,1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch and others in terms of line arrangements. They use branched covers over a suitable blow up of the complete quadrilateral arrangement of lines in projective 2-space to construct the complex hyperbolic surfaces over the orbifolds...

In this work we will build a fundamental domain for Deligne-Mostow lattices in PU(2,1) with 2-fold symmetry, which complete the whole list of Deligne-Mostow lattices in dimension 2. These lattices were introduced by Deligne and Mostow using monodromy of hypergeometric functions and have been reinterpreted by Thurston as authomorphisms on a sphere w...

Deligne and Mostow constructed a class of lattices in PU(2,1) using monodromy of hypergeometric functions. Later, Thurston reinterpreted them in terms of cone metrics on the sphere. In this spirit we construct a fundamental domain for almost all Deligne-Mostow lattices with three fold symmetry. This is a generalisation of the works of Parker and Bo...

We consider a symbolic coding for geodesics on the family of Veech surfaces (translation surfaces rich with affine symmetries) recently discovered by Bouw and M\"oller. These surfaces, as noticed by Hooper, can be realized by cutting and pasting a collection of semi-regular polygons. We characterize the set of symbolic sequences (cutting sequences)...

A cutting sequence is a symbolic coding of a linear trajectory on a translation surface corresponding to the sequence of sides hit in a polygonal representation of the surface. We characterize cutting sequences in a regular hexagon with opposite sides identified by translations exploiting the same procedure used by Smillie and Ulcigrai for the regu...