Joseph Maher is interested in geometric topology, particularly in the study of surfaces and three-dimensional spaces, and random walks on groups.  Other topics of interest include knots, hyperbolic geometry, and the collection of all maps from a surface to itself, which is known as the mapping class group of the surface. This group has interesting large scale geometry, and is closely related to the space of all hyperbolic metrics on a surface, known as Teichmüller space.


PhD University of California, Santa Barbara

BA Cambridge University

Scholarship / Publications

Random walks on weakly hyperbolic groups, with Giulio Tiozzo, arXiv:1410.4173.

Random methods in 3-manifold theory, with Alexander Lubotzky and Conan Wu, arXiv:1405.6410.

Word length statistics for Teichmüller geodesics and singularity of harmonic measure, with Vaibhav Gadre and Giulio Tiozzo, arXiv:1212.1481.

Exponential decay in the mapping class group, J. London Math. Soc. (2012) 86(2), 366-386, arXiv:1104.5543, correction.

Statistics and compression of scl, with Danny Calegari, Ergodic Theory and Dynamical Systems, arXiv:1008.4952.

Asymptotics for pseudo-Anosov elements in Teichmuller lattices, Geom. Funct. Anal. Vol. 20 (2010) 527-544, arXiv:0901.2679.

Random Heegaard splittings, Journal of Topology (2010) 3 (4), 997-1025, arXiv:0809.4881.

Linear progress in the complex of curves, Trans. Amer. Math. Soc. 362 (2010), 2963-2991, arXiv:0802.0467.

Random walks on the mapping class group, Duke Mathematical Journal, 156, Number 3 (2011), 429-468, arXiv:math/0604433.

Heegaard gradient and virtual fibers, Geometry and Topology, Vol. 9 (2005), 2227-2259, arXiv:math/0411219.

Period three actions on lens spaces, Alg. and Geom. Topol., Vol 7. (2007), 2021-2102, arXiv:math/0311009.

Period three actions on the three sphere, with Hyam Rubinstein, Geometry and Topology, Vol. 7 (2003), 329-397, arXiv:math/0204077.

Virtually embedded boundary slopes, Topology And Its Applications (95)1 (1999), 63-74, arXiv:math/9901041.