Jim Belk Bard College
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# Research

My primary research area is geometric group theory, the study of topological and geometric properties of infinite discrete groups, as well as the actions of infinite discrete groups on topological and geometric spaces. See Jon McCammond's geometric group theory page for an overview of the geometric group theory research community.

My research focuses primarily on the Thompson groups $$F$$, $$T$$, and $$V$$ and their relatives, including groups of synchronous and asynchronous automata such as the Grigorchuk group and iterated monodromy groups. I am most interested in connections between these groups and other areas of mathematics, including automata and formal languages, dynamical systems, and fractal geometry.

## Publications & Preprints

Here is a complete list of my papers and preprints. My collaborators include Collin Bleak, James Hyde, Francesco Matucci, Bradley Forrest, Sarah Koch, Dan Margalit, Rebecca Winarski, Justin Lanier, Brita Nucinkis, Conchita Martínez-Pérez, Robert McGrail, Nabil Hossain, Kai-Uwe Bux, and my Ph.D. advisor Kenneth Brown.

2017
Hyperbolic Dynamics and Centralizers in the Brin-Thompson Group $$\boldsymbol{2V}$$ (with C. Martínez-Pérez, F. Matucci, and B. Nucinkis). Manuscript in Preparation.
2017
Median Groups and Bass-Serre Theory for CAT(0) Cubical Complexes (with B. Forrest). Manuscript in Preparation.
2017
Rational Embeddings of Hyperbolic Groups (with C. Bleak and F. Matucci). Preprint (2017). arXiv:1711.08369.
2017
On the Asynchronous Rational Group (with J. Hyde and F. Matucci). Preprint (2017). arXiv:1711.01668.
2017
Embedding Right-Angled Artin Groups into Brin-Thompson Groups  (with C. Bleak and F. Matucci). Preprint (2017). Accepted to Mathematical Proceedings of the Cambridge Philosophical Society.
2017
Some Undecidability Results for Asynchronous Transducers and the Brin-Thompson Group $$\boldsymbol{2V}$$   (with C. Bleak). Transactions of the American Mathematical Society 369.5 (2017): 3157–3172.
2016
Rearrangement Groups of Fractals  (with B. Forrest). Preprint (2016). Accepted to Transactions of the American Mathematical Society.
2016
Röver's Simple Group is of Type $$\boldsymbol{F_\infty}$$   (with F. Matucci). Publicacions Matemàtiques 60.2 (2016), 501–552.
2015
The Word Problem for Finitely Presented Quandles is Undecidable  (with R. McGrail). In Logic, Language, Information, and Computation, pp. 1–13. Springer Berlin Heidelberg, 2015.
2015
A Thompson Group for the Basilica   (with B. Forrest) Groups, Geometry, and Dynamics 9.4 (2015): 975–1000.
2014
Implementation of a Solution to the Conjugacy Problem in Thompson's Group $$\boldsymbol{F}$$   (with N. Hossain, F. Matucci, and R. McGrail) ACM Communications in Computer Algebra 47.3/4 (2014): 120–121.
2014
CSPs and Connectedness: P/NP Dichotomy for Idempotent, Right Quasigroups   (with B. Fish, S. Garber, R. McGrail, and J. Wood) Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on, pp. 367–374. IEEE, 2014.
2014
Conjugacy and Dynamics in Thompson's Groups   (with F. Matucci) Geometriae Dedicata 169.1 (2014): 239–261.
2013
Deciding Conjugacy in Thompson's Group F in Linear Time   (with N. Hossain, F. Matucci, and R. McGrail) Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 15th International Symposium on. IEEE, 2013.
2010
Iterated Monodromy for a Two-Dimensional Map   (with S. Koch) In the Tradition of Ahlfors–Bers, V, 1–12, Contemporary Mathematics, 510, AMS 2010.
2005
Thompson's Group $$\boldsymbol{F}$$ is Maximally Nonconvex   (with K. Bux). Geometric methods in group theory, 131–146, Contemporary Mathematics, 372, AMS 2005.
2005
Forest Diagrams for Elements of Thompson's Group $$\boldsymbol{F}$$   (with K. Brown). International Journal of Algebra and Computation 15 (2005), no. 5–6, 815–850.
2004
Thompson's group $$\boldsymbol{F}$$   (Ph.D. thesis, Cornell University, supervised by K. Brown).