|Arxiv||Automorphisms of higher rank lamplighter groups (joint with Melanie Stein and Peter Wong) Internat. J. Algebra Comput. 25 no. 8, (2015), 1275–1299.|
|Arxiv||Tree-based language complexity of Thompson's group F (joint with Sharif Younes), Groups, Complexity, Cryptology 7 no. 2, (2015), 135–152.|
|Arxiv||Thompson's group F is 1-counter graph automatic (joint with Murray Elder), to appear in Groups, Complexity, Cryptology.|
|Arxiv||Bilipschitz versus quasi-isometric equivalence for higher rank lamplighter groups (joint with Tulliz Dymarz and Irine Peng), New York Journal of Mathematics Vol. 21 (2015), 129--150.|
|Arxiv||C-graph automatic groups (joint with Murray Elder), J. Algebra 413 (2014), 289–-319.|
|Arxiv||Metric Properties of Diestel-Leader Groups (joint with Melanie Stein), Michigan Math. J} Vol. 62 No. 2 (2013), 365--386.|
|Arxiv||Tame combings and Almost Convexity Conditions (joint with Sean Cleary, Susan Hermiller and Melanie Stein), Mathematische Zeitschrift Vol. 269 No. 3 (2011), 879--915.|
|Arxiv||Free limits of Thompson's group $F$ (joint with Azer Akhmedov and Melanie Stein), Geometriae Dedicata Vol. 155 No. 1 (2012), 163--176.|
|Arxiv||Tame combing and almost convexity conditions (joint with S. Cleary, S. Hermiller and M. Stein), Math Z. 269, no. 3 (2011), 879-915.|
|Arxiv||The geometry of twisted conjugacy classes in wreath products (joint with Peter Wong), in Benson Farb and David Fisher, editors, Geometry, Rigidity and Group Actions, Chicago Lectures in Math., Univ. Chicago Press, Chicago, IL, 2011, 561-–587.|
|Arxiv||A note on convexity properties of Thompson's group F (joint with Melanie Stein and Matthew Horak), to appear in the Journal of Group Theory.|
|Arxiv||Random subgroups of Thompson's group F (joint with Sean Cleary, Murray Elder and Andrew Reichnitzer), Groups Geom. Dyn. 4 (2010), no. 1, 91–126.|
|Arxiv||Computing word length in alternate presentations of Thompson's group F (joint with Melanie Stein and Matthew Horak), Internat. J. Algebra Comput. 19(2009), no. 8, 963-997.|
|Arxiv||A note on twisted conjugacy and generalized Baumslag-Solitar groups (joint with Peter Wong), preprint, 2006.|
|Arxiv||Twisted conjugacy and quasi-isomety invariance for generalized solvable Baumslag-Solitar groups (joint with Peter Wong), J. Lond. Math. Soc. (2) 75 (2007), no. 3, 705--717.|
|Arxiv||Combinatorial and metric properties of Thompson’s group T (joint with Jose Burillo, Sean Cleary and Melanie Stein, Trans. Amer. Math. Soc. 361 (2009), no. 2, 631--652.|
|Arxiv||Bounding right-arm rotation distances (joint with Sean Cleary), Internat. J. Algebra Comput.17 (2007), no. 2, 369--399.|
|Arxiv||Cone types and geodesic languages for lamplighter groups and Thompson's group F (joint with Sean Cleary and Murray Elder), J. Algebra, Vol. 303 No. 2 (2006), pp. 476-500.|
|Arxiv||Metric properties of the lamplighter group as an automata group (joint with Sean Cleary), in Jose Burillo, Sean Cleary, Murray Elder, Jennifer Taback and Enric Ventura, editors, Geometric Methods in Group Theory, American Mathematical Society, 2005.|
|Arxiv||Dead end words in lamplighter groups and other wreath products (joint with Sean Cleary), Quarterly Journal of Mathematics Volume 56 No. 2 (2005), pp.165-178.|
|Arxiv||Seesaw words in Thompson's group F (joint with Sean Cleary), in Jose Burillo, Sean Cleary, Murray Elder, Jennifer Taback and Enric Ventura, editors, Geometric Methods in Group Theory, American Mathematical Society, 2005.|
|Arxiv||The large scale geometry of some metabelian groups (joint with Kevin Whyte), Michigan Math. Journal, Vol. 52 No. 1 (2004), pp. 205-218.|
|Restricted rotation distance (joint with Sean Cleary), Information Proc. Letters, Vol. 88 No. 5 (2003), pp. 251-256.|
|New York Journal||Geometric quasi-isometric embeddings into Thompson's group F (joint with Sean Cleary), New York Journal of Mathematics, 9 (2003), pp. 141-148.|
|Arxiv||Combinatorial properties of Thompson's group F (joint with Sean Cleary), Trans. AMS. Vol. 356 No. 7 (2004), pp. 2825--2849 (electronic).|
|Arxiv||Thompson's group F is not almost convex (joint with Sean Cleary), J. Algebra, Vol. 270 No. 1 (2004), pp 133-149.|
|Surface symmetries and PSL(2,p) (joint with Murad Ozaydin and Charlotte Simmons), Trans. Amer. Math. Soc. 359(2007), 2243-2268.|
|New York Journal||Equivalence of geometric and combinatorial Dehn functions (joint with Jose Burillo), New York Journal of Mathematics, 8 (2002), pp. 169-179.|
|Arxiv||The Dehn function of PSL(2,Z[1/p]), Geom. Dedicata, Vol. 102 No. 1 (2003) pp. 179-195.|
|Arxiv||Quasi-isometric rigidity of PSL(2,Z[1/p]), Duke Math. Journal, 101 (2000), No. 2, pp. 335-357.|
Professor of Mathematics
Searles Science Building - 204
Teaching this semester
MATH 2020. Introduction to Mathematical Reasoning
An introduction to logical deductive reasoning and mathematical proof through diverse topics in higher mathematics. Specific topics include set and function theory, modular arithmetic, proof by induction, and the cardinality of infinite sets. May also consider additional topics such as graph theory, number theory, and finite state automata.
MATH 3602. Advanced Topics in Group Theory
The study of group actions on geometric objects; understanding finite and discrete groups via generators and presentations. Applications to geometry, topology, and linear algebra, focusing on certain families of groups. Topics may include Cayley graphs, the word problem, growth of groups, and group representations.
- Ph.D., University of Chicago (1998)
- MA, University of Chicago (1994)
- BA, Yale University (1993)
Field of Specialization
- Geometric and combinatorial group theory
I am a member-at-large of the Council of the American Mathematical Society and a member of its Executive Committee.
American Mathematical Society Eastern Sectional Meeting at Bowdoin College
On September 24-25, 2016, Bowdoin College will host the American Mathematical Society Eastern Sectional Meeting.
- Plenary lectures given by Moon Duchin (Tufts), Thomas Lam (Michigan) and Tim Austin (NYU).
- Community Mathematics Lecture on Saturday, Sept. 24 at 8:00pm. Speaker TBA.
- Lobster dinner! (Must register in advance on the Bowdoin web page, link below.)
Click here for the AMS conference web page.
Click here for the Bowdoin College conference web page with information about dining, Brunswick, ME, and weekend activities.
During the Spring 2016 semester I am teaching two sections of Introduction to Mathematical Reasoning.
- Section A: Tuesday/Thursday 10:00-11:30am
- Section B: Tuesday/Thursday 1:00-2:30pm