Jim Belk

August 2004

**Ph.D., Cornell University**, Mathematics

May 2002

**M.S., Cornell University**, Mathematics

May 1999

**M.A., Binghamton University**, Mathematics

May 1998

**B.A., Binghamton University**, Mathematics and Physics

Fall 2017 – Present

Fall 2016 – Present

Fall 2010 – Spring 2016

Fall 2008 – Spring 2010

**Bard College**

*Mathematics Program Chair*

*Associate Professor*, Mathematics Program

*Assistant Professor*, Mathematics Program

*Visiting Assistant Professor*, Mathematics Program

Fall 2005 – Spring 2008

**Texas A&M University**

*NSF Postdoctoral Fellow*, Department of Mathematics

Fall 2004 – Spring 2005

**Cornell University**

*Visiting Assistant Professor*, Department of Mathematics

**Main Research Areas**

Geometric Group Theory, Dynamical Systems

**Other Research Interests**

Geometric topology, fractal geometry, automata theory, graph theory, discrete geometry.

Click on the icon to download the corresponding manuscript.

- 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).

Slides for recent talks can be found at math.bard.edu/belk/talks.htm.

January 2017

**“Rearrangement Groups of Self-Similar Spaces”**

Pure Mathematics Colloquium, University of St Andrews

August 2016

**“Rearrangement Groups of Fractals”**

Invited Address, *Workshop on the Thompson Groups*, University of Southern Denmark

April 2015

**“Rearrangement Groups of Fractals”**

Geometry and Topology Seminar, Binghamton University

May 2014

**“Dynamics and Decidability in Brin's Group \(\boldsymbol{2V}\)”**

Invited address, *Workshop on the Extended Family of R. Thompson’s Groups*, University of St. Andrews

**“Thompson-Like Groups for Self-Similar Structures”**

May 2014

Invited address, *Workshop on the Extended Family of
R. Thompson’s Groups*, University of St. Andrews

**“Turing Machines, Automata, and the Brin-Thompson Group \(\boldsymbol{2V}\)”**

November 2013

Algebra/Topology Seminar, SUNY Albany

October 2013

Oberseminar Gruppen und Geometrie, Universität Bielefeld

October 2013

Groupes de Travail de L'équipe Topologie Dynamique, Départment de Mathématiques d’Orsay, Université Paris-Sud

October 2013

Pure Mathematics Colloquium, University of St Andrews

September 2013

Geometry and Topology Seminar, Binghamton University

**“Thompson-Like Groups Acting on Julia Sets”**

October 2013

Analysis Research Group, University of St Andrews

August 2013

*Groups St Andrews 2013*, University of St Andrews

April 2013

**“Symmetries of Julia Sets”**

Mathematics Seminar, Hamilton College

**“A Thompson Group for the Basilica”**

April 2013

AMS Special Session on Arithmetic Dynamics and Galois Theory, 2013 Spring Eastern Sectional Meeting at Boston College

April 2012

Algebra Seminar, University of Virginia

April 2012

Geometry and Topology Seminar, Binghamton University

**“Braids without Twists”**

January 2008

AMS Special Session on Algebra and Group Theory, 2008 Joint Mathematics Meetings in San Diego, California.

**“Conjugacy and Dynamics in Thompson's Groups”**

October 2008

Topology/Geometry Seminar, Rutgers University

April 2007

Topology Seminar, University of Virginia

April 2007

Topology & Geometric Group Theory Seminar, Cornell University

**“Forest Diagrams for Thompson’s Group \(\boldsymbol{F}\)”**

October 2004

Geometry and Topology Seminar, Binghamton University

October 2003

AMS Special Session on Geometric Group Theory, 2003 Fall Eastern Sectional Meeting at Binghamton University

June 2003

International Conference on Group Theory in Gaeta, Italy

This is a list of all courses I have taught and tutorials (i.e. reading courses) I have supervised while at Bard College. See http://math.bard.edu/courses for course descriptions.

Upper-Level Courses | |
---|---|

Math 312: Advanced Calculus (F17) | Math 314: Mathematical Modeling (F16) |

Math 318: Number Theory (S16) | Math 351: Topology (F10, S15) |

Math 323: Dynamical Systems (F08, S11, F12, F14, F15) |
Math 332: Abstract Algebra (S09, S10, S13) |

Math 352: Diff. Geometry (F11, F14) | Math 361: Real Analysis (S12, S18) |

Math 362: Complex Analysis (S18) | Math 461: Real Analysis II (S11, S16) |

Lower-Level Courses | |

FYSEM: First-Year Seminar (S17) | Math 108: Secret Codes (S15) |

Math 141: Calculus I (S13, S12, F08) | Math 142: Calculus II (F09, F17) |

Physics 142: Physics II (S09, S10) | Math 212: Calculus III (F11) |

Math 213: Linear Algebra w/ ODE's ( F12, S14, F15, S17) |
Math 241: Vector Calculus (S14, F16) |

Math 261: Proofs & Fund. (F10) | |

Math 299: Prob.-Solv. Sem. (F09) | |

Tutorials | |

Geom. Group Theory: 3 students (F17) | Functional Analysis: 1 student (F16) |

Applied Math: 1 student (F15) | Advanced Real Analysis 3 students (S13), 1 student (S14) 3 students (S15), 2 students (S17) |

Represent. Theory: 3 students (F14) | |

Algebraic Topology: 1 student (F11) | |

Research Tutorial: 3 students (F10) | Advanced Abstract Algebra 1 student (S09), 1 student (F09) 1 student (S10), 2 students (S13) 1 student (F16) |

Diff. Geometry: 1 student (F09) | |

Complex Analysis: 2 students (S09) |

All students at Bard College complete a year-long research project during their senior year. I have supervised 17 such projects, covering a wide variety of topics. Projects marked with a star (*) are directly related to my research.

- 2016
- *Cyril Kuhns, “Public-Key Cryptography with the Brin-Thompson Group \(2V\)” (with Robert McGrail)
- Nicole Song, “A Variational Approach to the Moving Sofa Problem”
- 2015
- *Shuyi Weng, “Homeomorphism Groups of Fractals”
- Van Mai Nguyen Thi, “Development and Optimization of a Two-View Model for Anamorphic Projections on Planar Surfaces” (with Keith O'Hara)
- Sharma Maharaj, “Resistance of Infinite Networks”
- 2014
- Andy Huynh, “Geometry of Adinkra Embeddings” (with Greg Landweber)
- Lara Merling, “Fighting Fires on Semi-Regular Tessellations” (with Lauren Rose)
- 2013
- Abhinanda Bhattacharyya, “Forbidden Minors for a Pursuit Game on Graphs”
- *Nabil Hossain, “Implementation of the Solution to the Conjugacy Problem in Thompson's Groups” (with Robert McGrail)
- *Will Smith, “Thompson-Like Groups for Dendrite Julia Sets”
- *Jasper Weinrich-Burd, “A Thompson-Like Group for the Bubble Bath Julia Set”
- 2012
- Kimberly Wood, “Switching the Shannon Switching Game”
- Zhiwei Wu, “Computable Invariants for Quandles” (with Robert McGrail)
- 2011
- *Adam Chodoff, “Twisted Three-Eared Rabbits: Identifying Topological Quadratics up to Thurston Equivalence”
- Alexandros Fragkopoulos, “Electron Scattering in Crossed Electric and Magnetic Fields: A Semiclassical Study” (with Christian Bracher)
- 2010
- *Cedric Cogell, “Finding Følner Sets Automatically”
- Huaizhou Jin, “SLAM on a Graph through Recursive Filtering”
- 2009
- Paul McLaughlin, “Chaos in Bird Vocalizations”
- *Nick Michaud, “A Three-Element Generating Set for Thompson's Group \(F\)”

**“Symmetries of Fractals”**

Spring 2017

Bard Mathematics Seminar

**“Geometry of Infinite Graphs”**

November 2013

Richard Stockton College Mathematics Seminar

July 2011

2011 Canada/USA Mathcamp, Reed College

July 2010

Bard Summer REU

November 2008

Bard Mathematics, Computer Science, and Physics Seminar

**“Game Theory”** (joint with Maria Belk)

July 2012

Bard Summer Workshop for School Math Teachers

**“Symmetries of Julia Sets”**

February 2012

Bard Mathematics, Computer Science, and Physics Seminar

**“Fractal Geometry”**

October 2011

Public Lecture, Bard Lifetime Learning Institute

August 2009

Language & Thinking Program, Bard College

August 2008

Language & Thinking Program, Bard College

**“Tensegrities”** (joint with Maria Belk)

July 2011

Bard Summer Workshop for School Math Teachers

**“Dynamical Systems”** (joint with Sarah Koch)

July 2011

Five-day-long minicourse at Mathcamp 2011, Reed College

**“Fractals, Dynamics, and Julia Sets”**

November 2010

Richard Stockton College Mathematics Seminar

April 2008

Bard Mathematics, Computer Science, and Physics Seminar

**“Pythagoras in Spherical and Hyperbolic Geometry”** (joint with Maria Belk)

July 2010

Bard Summer Workshop for School Math Teachers

- Mathematics Program Chair, Fall 2017–Present
- Search Committee for Mathematics Position, Fall 2017–Spring 2018
- Faculty Education and Oversight Committee for Bard College Berlin, Spring 2015–Present
- Organizer, Math Subject GRE Review Sessions at Bard College (F11, F12, F17)
- Conducted Joint Meetings Interviews for Mathematics Position, January 2016
- Putnam Exam Coordinator for Bard College (F12, F16)
- Bard Council for Inclusive Excellence, Fall 2015–Present
- Bard College Diversity Committee, Fall 2014–Spring 2017
- Superadviser during first-year registration at Bard College (F09, F10, F11, F12, F15)
- Coordinated Mathematics Moderation Boards (S17, F16, S16, F15, S15, F14, S14, S13)
- Bard College Campus Facilities Committee, 2011–2013
- Physics Working Group 2011
- Organizer, Bard College Mathematics/Physics/Computer Science Seminar, 2009–2011

- •
*Transactions of the American Mathematical Society* - •
*Algebraic & Geometric Topology* - •
*Geometriae Dedicata* - •
*Journal of Group Theory* - • 3rd Bi-Annual Mid-Hudson Mathematics Conference for Undergraduates (October 2011)
- • 2nd Bi-Annual Mid-Hudson Mathematics Conference for Undergraduates (October 2009)
- • 2008 Discrete Mathematics Day at Bard College (November 2008)

**Refereeing**

I have refereed papers for the following journals:

**Conferences Organized**

I have been a co-organizer for three conferences at Bard college:

**Stack Exchange**

I contribute to several sites on the Stack Exchange network, including Math Overflow, Math Stack Exchange, and Math Educators Stack Exchange. You can see a list of my questions and answers at the following link.