Under Review

(With V. Markovic and I. Smilga) Geometrically and topologically random surfaces in a closed hyperbolic three manifold.

Awaiting Publication

(With F. Labourie and S. Mozes) Surface groups in uniform lattices of some semi-simple groups. To appear in Acta Mathematica.

Published papers

(With T. Firsova and N. Selinger) On deformation spaces of quadratic rational functions. International Mathematics Research Notices, (2022)

(With D. Thurston and K. Pilgrim) Conformal surface embeddings and extremal length. Groups, Geometry, and Dynamics, 16 (2022), 403–435

(With A. Wright) Hodge and Teichmuller. Journal of Modern Dynamics, 18 (2022), 149-160

(With A. Wright) Nearly Fuchsian surface subgroups of finite covolume Kleinian groups. Duke Mathematics Journal 170 (2021), 503-573

(With V. Markovic) The good pants homology and the Ehrenpreis conjecture. Annals of Mathematics, 182 (2015), 1-72

(With V. Markovic) Counting essential surfaces in a closed hyperbolic three-manifold. Geometry & Topology, 16 (2012), 601–624

(With V. Markovic) Immersing almost geodesic surfaces in a closed hyperbolic three-manifold. Annals of Mathematics, 175 (2012), 1127-1190

(With M. Bridgeman) Hyperbolic volume of manifolds with geodesic boundary and orthospectra. Geometric and Functional Analysis 20 (2010), 1210–1230

(With M. Lyubich) A priori bounds for some infinitely renormalizable quadratics: II. Decorations. Annales scientifiques de l'École Normale Supérieure, 41 (2008), 57-84

(With M. Lyubich) A priori bounds for some infinitely renormalizable quadratics: III. Molecules. In Complex Dynamics: Families and Friends, (2009), 229-254

(With M. Lyubich) The Quasi-additivity Law in Conformal Geometry. Annals of Mathematics, 169 (2009) 561-593

(With M. Lyubich) Local connectivity of Julia sets for unicritical polynomials. Annals of Mathematics, 170 (2009), 413-426

(With A. Avila, M. Lyubich, and W. Shen) Combinatorial rigidity for unicritical polynomials. Annals of Mathematics, 170 (2009), 783-797

Papers that have not been formally published

(With V. Markovic) The Weil-Petersson distance between finite degree covers of punctured Riemann surfaces. What happened to this paper.

A priori bounds for some infinitely renormalizable quadratics: I. Bounded primitive combinatorics. Why this paper has not appeared in a journal.

Holomorphic Removability of Julia Sets. What happened to this paper.

Short papers and notes

The Mandelbrot set is Connected: A topological proof.


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