Jim Belk

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.

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- 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**(with N. Hossain, F. Matucci, and R. McGrail)*F*in Linear Time*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).