Research

LIST OF PUBLICATIONS:

1. Dynamics and geometry of character varieties for surface groups  (with D. Chasteen-Boyd, S. Schlich), arXiv:2607.06473, to appear in the book In the Tradition of Thurston IV.

2. d-pleated surfaces and their shear-bend coordinates (with G. Martone, F. Mazzoli, T. Zhang), arXiv:2305.11780, to appear in Proceeding of the London Mathematical Society. 

3. Constructing reducibly geometrically finite subgroups of the mapping class group (with T. Aougab, H. Bray, S. Dowdall, H. Hoganson, B. Whitfield), arXiv:2501.13234, to appear in Groups, Geometry and Dynamics. 

4. Dynamics on the SU(2,1)-character variety of the one-hole torus (with S. Lawton, F. Palesi),  arXiv:2402:10838, to appear in Moduli.

5. Fiber bundles associated with Anosov representations (with D. Alessandrini, N. Tholozan, A. Wienhard), arXiv:2303.10786, to appear in Forum of Mathematics, Sigma.

6. 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. 

7. 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.

8.  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.

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

10. 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.

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

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

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

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

15. 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. Topology of the space of $d$-pleated surfaces (with G. Martone, F. Mazzoli, T. Zhang), arXiv:2508.04813. 

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

IN PREPARATION:

1. On parabolically geometrically finite subgroups of the mapping class group, with S. Dowdall, T. Weisman, in preparation.

2. On harmonic maps with polynomial Hopf differential, with L. Nguyen, N. Sagman, in preparation.

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

4. Mapping class group action on SU(3)-character varieties of punctured surfaces, with D. Chasteen-Boyd, S. Lawton, F. Palesi, in progress.

5. Combination theorems for extended convergence actions, with T. Weisman, in progress. 

6. Geometric limits of semi-simple Lie groups, 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.