Not yet on the arxiv:

• Random walks on the mapping class group.
  This is a rewrite of the arxiv paper, hopefully more comprehensible, but without the result about hyperbolic manifolds. (New version as of 03/23/08 fixes mistake in final section, and some of the semigroups were the wrong way round.)
• Random Heegaard splittings.
  This contains the result about hyperbolic manifolds, and fixes a serious gap in the original version, pointed out by the referee.

Papers:

• Linear progress in the complex of curves, arXiv:math/0802.0467.
• Random walks on the mapping class group, arXiv:math/0604433.
• Heegaard gradient and virtual fibers, Geometry and Topology, Vol. 9 (2005), pages 2227-2259, arXiv:math/0411219.
• Period three actions on lens spaces, Alg. and Geom. Topol., Vol 7 (2007), pages 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.

Normally I try and write on blackboards, but here are the slides I've made for various talks.

• "Random Heegaard splittings," AMS joint meeting, San Diego, January 2008.
• "Linear progress in the complex of curves," Spring Topology and Dynamics Conference, Rolla, Missouri, March 2007.
• "Random walks on the mapping class group," Hyperbolic Geometry Workshop, Fields Institute, Toronto, May 2006.
• "Heegaard splittings and virtual fibers," AMS Sectional Meeting, Santa Barbara, April 2005
• "Period three actions on the three sphere," Wasatch Topology Conference, Park City, June 2003.

Here is a short overview of my thesis, intended for a general audience.

• Period three tilings of the three sphere.

• Period three actions on the three sphere are standard (with Hyam Rubinstein).

My Erdös number is 3: Maher - Rubinstein - Wormald - Erdös.