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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 non-orientable.

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 non-orientable surfaces, V. Erlandsson, M. Gendulphe, I. Pasquinelli, J. Souto, to appear in Geometric and Functional Analysis, also available here.

[5.] Representations of Deligne-Mostow lattices into PGL(3, C), E. Falbel, I. Pasquinelli, A. Ucan-Puc, 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 Bouw-Möller surfaces: an S-adic characterization, D. Davis, I. Pasquinelli, C. Ulcigrai, Annales scientifiques de l'Ecole Normale Supérieure (4), 52:4 (2019), 927-1023, also available here.

[2.] Fundamental domains and presentations for the Deligne-Mostow lattices with 2-fold symmetry , I. Pasquinelli, Pacific Journal of Mathematics 302:1 (2019), 201-247, also available here.

[1.] Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere, I. Pasquinelli, Conformal Geometry and Dynamics 20 (2016), 235-281, also available here.

Others

[c.] Representations of Deligne-Mostow lattices into PGL(3, C) part II, E. Falbel, I. Pasquinelli, A. Ucan-Puc, 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.