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Papers.

1. Quotients of the curve complex, with Hidetoshi Masai and Saul Schleimer, Groups, Geometry and Dynamics 18 (2024), no. 2, 379—405, arXiv:2010.13360.

2. Random trees in the boundary of Outer space, with Ilya Kapovich, Catherine Pfaff, and Samuel J. Taylor, Geometry and Topology, 26 (2022) 127—162, arXiv:1904.10026.

3. Random walks, WPD actions, and the Cremona group, with Giulio Tiozzo, Proceedings of the London Mathematical Society, Volume 123, Issue 2, August 2021, 153—202, arXiv:1807.10230.

4. Random outer automorphisms of free groups: Attracting trees and their singularity structures, with Ilya Kapovich, Catherine Pfaff, and Samuel J. Taylor, Transactions of the American Mathematical Society, 375 (2022), 525—557, arXiv:1805.12382.

5. The compression body graph has infinite diameter, with Saul Schleimer, Algebraic and Geometric Topology, 21 (2021) 1817—1856, arXiv:1803.06065.

6. Morse functions to graphs and topological complexity for hyperbolic 3-manifolds, with Diane Hoffoss, Communications in Analysis and Geometry, Vol. 30 (2022), no. 4, 843—868, arXiv:1708.04140.

7. Recurrence of quadratic differentials for harmonic measure, with Vaibhav Gadre, Mathematical Proceedings of the Cambridge Philosophical Society, 169 (2020), no. 2, 299—305, arXiv:1706.01926.

8. Random subgroups of acylindrically hyperbolic groups and hyperbolic embeddings, with Alessandro Sisto, International Mathematics Research Notices, Vol. 2019 (13) 3941—3980, arXiv:1701.00253.

9. The stratum of random mapping classes, with Vaibhav Gadre, Ergodic Theory and Dynamical Systems, (2018) Vol. 38 (7) 2666—2682, arXiv:1607.01281.

10. Morse area and Scharlemann-Thompson width for hyperbolic 3-manifolds, with Diane Hoffoss, Pacific Journal of Mathematics, Vol. 281 (2016) No. 1, 83—102, arXiv.org:1503.08521.

11. Random walks on weakly hyperbolic groups, with Giulio Tiozzo, Journal für die reine und angewandte Mathematik (Crelle’s Journal), Vol. 2018, Issue 742, 187—239, arXiv:1410.4173.

12. Random methods in 3-manifold theory, with Alexander Lubotzky and Conan Wu, Proceedings of the Steklov Institute of Mathematics, 2016, Vol. 292, 118—142, arXiv:1405.6410.

13. Word length statistics for Teichmüller geodesics and singularity of harmonic measure, with Vaibhav Gadre and Giulio Tiozzo, Commentarii Mathematici Helvetici 92 (2017), no. 1, 1—36., arXiv:1212.1481.

14. Word length statistics and Lyapunov exponents for Fuchsian groups with cusps, with Vaibhav Gadre and Giulio Tiozzo, New York Journal of Mathematics, Volume 21 (2015) 511—531.

15. Exponential decay in the mapping class group, Journal of the London Mathematical Society, (2012) 86(2), 366—386, arXiv:1104.5543, correction.

16. Statistics and compression of scl, with Danny Calegari, Ergodic Theory and Dynamical Systems, (2015) volume 35(1), issue 01, pp. 64—110, arXiv:1008.4952.

17. Asymptotics for pseudo-Anosov elements in Teichmuller lattices, Geometric and Functional Analysis, Vol. 20 (2010) 527—544, arXiv:0901.2679.

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

19. Linear progress in the complex of curves, Transactions of the American Mathematical Society, 362 (2010), 2963—2991, arXiv:0802.0467.

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

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

22. Period three actions on lens spaces, Algebraic and Geometric Topology, Vol 7. (2007), 2021—2102, arXiv:math/0311009.

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

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

Acknowledgements.

• Research supported by NSF grant DMS-070674, Simons Foundation CGM 234477, CGM 579762, PSC-CUNY grants PSCOOC-41-80, TRADB-43-20, TRADB-44-178, TRADB-45-17, TRADB-46-3, TRADB-47-2, TRADB-50-260 and TRADB-51-242, TRADB-53-2.

Graduate Students.

• Matt Sunderland (2018).

Talks.

Normally I try and write on blackboards, but here are the slides I’ve made for various talks, and some video recordings.

• “Singularity of measures for Cannon-Thurston maps”, Nonlinear Days 2024: Dynamics of Group Actions and Random Walks on Groups, Fields Institute, May 2024.

• “Singularity of measures for Cannon-Thurston maps”, Knot Theory Informed by Random Models and Experimental Data, Banff, April 2024.

• “Singularity of measures for Cannon-Thurston maps”, GAGTA, Vienna, July 2023.

• “Random walks on groups with negative curvature”, FoCM, Barcelona, Jul 2017.

• Random walks on groups with hyperbolic properties, Notre Dame, May 2015.
  Lecture 1, Lecture 2, Lecture 3, Lecture 4.

• “Casson invariants for random Heegaard splittings,” AMS Meeting, Baltimore, Mar 2014.

• “Random walks on groups,” Stochastic Processes and their Applications 2013, Boulder, Aug 2013.

• “Statistics for Teichmuller geodesics,” Spring Topology and Dynamics Conference, CCSU, Mar 2013.

• “Exponential decay in the mapping class group,” AMS Joint Meeting, Jan 2012.

• “Random walks on graphs and groups,” Bowling Green State, April 2011.

• “Growth rates for stable commutator length,” AMS meeting, Holy Cross, April 2011.

• “Random Heegaard splittings,” Jacofest, Oklahoma State University, June 2010.

• “Asymptotics for pseudo-Anosovs in Teichmuller lattices,” AMS meeting, NJIT, May 2010.

• “Random Heegaard splittings,” AMS meeting, NJIT, May 2010.

• “Asymptotics for pseudo-Anosovs in Teichmuller lattices,” UIUC, March 2009.

• “Random walks on the mapping class group,” Hiroshima/Tokyo Tech/Nihon, Japan, May 2008.

• “Heegaard splittings and virtual fibers,” Nara/Hiroshima, Japan, May 2008.

• “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 meeting, Santa Barbara, April 2005.

• “Period three actions on the three sphere,” Wasatch Topology Conference, Park City, June 2003.

Miscellaneous.

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

• Period three tilings of the three sphere.

Here is the preprint version of the period three actions paper, with the original pictures, and an index.

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

My ORCID ID is 0000-0003-3391-1671.

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