Research

LIST OF PUBLICATIONS:

1. Geometric limits of cyclic subgroups of SO_0(1, k+1) and SU(1, k+1) (with B. Pozzetti), Algebraic and Geometric Topology 22-3 (2022), 1461-1495, pdf. 

2. Quasicircles and width of Jordan curves in CP^1 (with F. Bonsante, J. Danciger, J.-M. Schlenker), Bulletin of the London Mathematical Society 53 (2021), 507–523, pdf.

3.  The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti de Sitter geometry (with F. Bonsante, J. Danciger, J.-M. Schlenker), Geometry and Topology 25 (6) (2021), 2827--2911, pdf.

4. c-gluing construction and slices of quasi-Fuchsian space, Geometriae Dedicata 212(1),(2021), 107-139, pdf.

5. On type-preserving representations of the thrice punctured projective plane group (with F. Palesi, T. Yang), Journal of Differential Geometry 119 (2021),421-457, pdf.

6.  On the character varieties of the three-holed projective plane (with F. Palesi), Conformal Geometry and Dynamics 24 (2020), 68–108, pdf.

7.  Polyhedra inscribed in a quadric (with J. Danciger, J.-M. Schlenker), Inventiones Mathematicae 121 (1) (2020), 237-300, pdf.

8. On the character varieties of the four-holed sphere (with F. Palesi, S. P. Tan), Groups, Geometry, and Dynamics 9 (3) (2015), 737-782, pdf.

9. The asymptotic directions of pleating rays in the Maskit embedding, Conformal Dynamics and Hyperbolic Geometry, AMS Contemporary Mathematics, (2012), pdf.

10. Top terms of polynomial traces in Kra's plumbing construction (with C. Series), Algebraic and Geometric Topology 10 (3) (2010), 1565-1607, pdf.

• Slices of Quasifuchsian space, Ph.D. thesis, (2013), pdf.

PREPRINTS:

1. d-pleated surfaces and their shear-bend coordinates (with G. Martone, F. Mazzoli, T. Zhang), arXiv:2305.11780.

2. Fiber bundles associated with Anosov representations (with D. Alessandrini, N. Tholozan, A. Wienhard), arXiv:2303.10786.

3. Higher signature Delaunay decompositions (with J. Danciger, J.-M. Schlenker), arXiv:1602.03865.

IN PREPARATION:

1. Dynamics on the SU(2,1)-character variety of the one-hole torus (with S. Lawton, F. Palesi),  in preparation.

2. Bending lamination theorem for punctured-torus groups in anti-de Sitter space and geometric transition, with F. Gueritaud, in progress.

3. Geometric limits of cyclic Anosov representations, with B. Pozzetti, in progress.

NOTES:

1. Compactifications of Teichmuller space, notes from Cabin Conference, pdf.

2. Quasi-Fuchsian manifolds in hyperbolic, anti-de Sitter geometry and for higher rank Lie groups, minicourse 1 and minicourse 2, exercises, partial solutions.