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Irene Pasquinelli's research page
My project in complex hyperbolic geometry is about the study of discrete groups
in PU(n,1), the group of holomorphic isometries of complex hyperbolic space.
The complex hyperbolic space is a generalisation to complex numbers of
the real hyperbolic space and one would like to ask the same questions
about discrete groups that we have been investigating
for years in the real case.
But the usual techniques for real hyperbolic space not always work,
which makes this field rather exciting!
My project in curves counting is about looking at
curves of a given length on a hyperbolic surface
and trying to see how this number grows with the length.
While there is a lot of theorems known when the surface is orientable,
most techniques fail when the surface is nonorientable.
My project in dynamics on translation surfaces is about the study of cutting sequences
on Veech surfaces.
Given a polygonal representation for the surface,
one can code a trajectory with the sequences of sides hit.
Then, given a sequence in that alphabet, can we determine if it comes from a trajectory?
And if so, can we recover the direction of the trajectory?
All of my papers are on the arxiv.
Publications and preprints

[6.]
Mapping class group orbit closures for nonorientable surfaces,
V. Erlandsson,
M. Gendulphe,
I. Pasquinelli,
J. Souto,
to appear in Geometric and Functional Analysis,
also available here.

[5.]
Representations of DeligneMostow lattices into PGL(3, C),
E. Falbel, I. Pasquinelli,
A. UcanPuc,
to appear in Experimental Mathematics,
also available
here.

[4.]
Complex hyperbolic orbifolds and hybrid lattices,
E. Falbel, I. Pasquinelli,
Geom Dedicata 217, 28 (2023),, also available
here.

[3.]
Cutting sequences on BouwMöller surfaces: an Sadic characterization,
D. Davis, I. Pasquinelli,
C. Ulcigrai,
Annales scientifiques de l'Ecole Normale Supérieure
(4), 52:4 (2019), 9271023,
also available
here.

[2.]
Fundamental domains and presentations for the DeligneMostow lattices with 2fold symmetry
,
I. Pasquinelli,
Pacific Journal of Mathematics 302:1 (2019), 201247,
also available
here.

[1.]
DeligneMostow lattices with three fold symmetry and cone metrics on the
sphere,
I. Pasquinelli,
Conformal Geometry and Dynamics 20 (2016), 235281,
also available
here.
Others

[c.]
Representations of DeligneMostow lattices into PGL(3, C) part II,
E. Falbel, I. Pasquinelli,
A. UcanPuc,
available
here.

[b.]
Complex hyperbolic lattices and moduli spaces of flat surfaces,
I. Pasquinelli,
my PhD thesis under the supervision of
Prof. J. R. Parker,
available
here.

[a.]
Cutting sequences in Veech surfaces,
I. Pasquinelli,
my Master thesis under the supervision of
Prof. C. Ulcigrai,
available
here.