Research
My primary research interests are in Geometric Group Theory and Low Dimensional Topology.
My areas of interest include outer automorphism groups, intersections of graph theory and group theory (especially random graphs), algorithms in group theory, Artin and Coxeter groups, mapping class groups, 3-manifolds and asymptotic geometry of groups.
I received my Ph.D. in 2014 from CUNY Graduate Center under Jason Behrstock.
Papers and Preprints
Morse subgroups and boundaries of random right-angled Coxeter groups. To appear in Geometriae Dedicata.
Square percolation and the threshold for quadratic divergence in random right-angled Coxeter groups. With Jason Behrstock and Victor Falgas-Ravry. To appear in Random Structures & Algorithms. arXiv:2009.14442.
Automaticity for graphs of groups. With Susan Hermiller, Derek Holt and Sarah Rees. To appear in Groups, Geometry and Dynamics. arXiv:1905.05943.
Outer automorphism groups of graph products of abelian groups: subgroups and quotients. With Andrew Sale. To appear in Pacific Journal of Mathematics. arXiv:1902.01438.
Outer automorphism groups of a right-angled Coxeter groups are either large or virtually abelian. With Andrew Sale. Transactions of the American Mathematical Society 372 (2019), no. 11, pp. 7785--7803.
Geometry of the word problem for 3-manifold groups. With Mark Brittenham and Susan Hermiller. Journal of Algebra 499 (2018) pp. 111--150.
On hierarchical hyperbolicity of cubical groups. With Mark Hagen. Israel Journal of Mathematics 236 (2020), no.1, pp. 45--89.
Global structural properties of random graphs. With Jason Behrstock, Victor Falgas-Ravry, Mark Hagen. International Mathematics Research Notices (2018), no. 5, pp. 1411--1441.
Source code and data from the paper can be found here.
Stable commutator length in amalgamated free products. Journal of Topology and Analysis 7 (2015), no. 4, pp. 693--717.
Ph.D. Thesis: Stable commutator length in amalgamated free products. CUNY Graduate Center Ph.D. Thesis, April 2014
Recent/Upcoming Talks and Conferences
Binghamton Geometric Topology Seminar, November 2021
UNL Groups Semigroups and Topology Seminar, October 2021
CUNY Geometry and Topology, September 2021
GAGTA 14, June 2021 (20 minute contributed talk)
New York Group Theory Seminar, April 2021
Tufts University Geometric Group Theory and Topology Seminar, April 2019
Columbia University Geometric Topology Seminar, March 2019
University of Nebraska GST Seminar, October 2018
AMS Spring Midwest Sectionals Meeting: Special Session on Boundaries and Non-positive Curvature in Group Theory, April 2018
Cornell Topology Seminar, March 2018
CUNY Geometry and Topology Seminar, October 2017
Albany Algebra/Topology Seminar, October 2017
Slides and Notes from Invited Talks
Geometric Properties of Random Right-angled Coxeter Groups – New York Group Theory Seminar, April 2021
Outer Automorphism Groups of Right-angled Coxeter Groups – AMS Spring Sectionals, Vanderbilt University, April 2018.
Factor Systems and Hierarchical Hyperbolicity for CAT(0) Cube Complexes – Spring Topology and Dynamics Conference, March 2017.
Flows, Dynamics and Algorithms for 3-Manifold Groups – South Eastern Logic Symposium, University of Florida, March 2017.
The Geometry of Random Right-angled Coxeter Groups – Spring Topology and Dynamics Conference, May 2015
Stable Commutator Length in Amalgamated Free Products – GST Seminar, Lincoln Nebraska, April 2014.
Stable Commutator Length and Knot Complements – AMS Eastern Sectionals Conference, Temple University – October 2013.
An Introduction to Non-positive Curvature – Cubical Geometry and Right-Angled Artin Groups Reading Seminar, CUNY Graduate Center – September 2012
Uniform Compactness and Gromov's Embedding Theorem – Metric Geometry Reading Seminar, CUNY Graduate Center – June 2012
The Coarse Geometry of Groups – Group Theory course, CUNY Graduate Center – Fall 2011
Research Related Links
Jason Behrstock maintains a page about Random Graphs in Group Theory with a cool Java applet to visualize random graphs.
Part of the work above are/were supported by the National Science Foundation through the MPS-LEAPS program under Award No. 2137608.
The evolution of a random right-angled Coxeter group. All results above are classical or come from work cited above or work of Behrstock, Hagen and Sisto.