Jim Belk
Cornell University

**Cornell University**

Ph.D. Mathematics, August 2004

M.S. Mathematics, May 2002

**Binghamton University**

M.A. Mathematics, May 1999

B.S. Mathematics and Physics, May 1998

Fall 2021 – Spring 2022

**Cornell University**

*Visiting Assistant Professor*, Department of Mathematics

Fall 2018 – Spring 2021

**University of St Andrews**

*Research Fellow*, School of Mathematics and Statistics

Fall 2017 – Spring 2018

Fall 2016 – Spring 2018

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.

**Stabilizers in Higman–Thompson Groups**

with James Hyde and Francesco Matucci.

Preprint (2021). arXiv:2104.05572.**Conjugator Length in Thompson's Groups**

with Francesco Matucci.

Preprint (2021). arXiv:2101.10316.**Recognizing Topological Polynomials by Lifting Trees**

with Justin Lanier, Dan Margalit, and Rebecca R. Winarski.

Preprint (2020). Accepted to*Duke Mathematical Journal*. arXiv:1906.07680.**Embedding Q into a Finitely Presented Group**

with James Hyde and Francesco Matucci.

Preprint (2020). Accepted to*Bulletin of the American Mathematical Society*. arXiv:2005.02036.**Twisted Brin–Thompson Groups**

with Matthew C. B. Zaremsky.

Preprint (2020). Accepted to*Geometry & Topology*. arXiv:2001.04579.- 2021
**Rational Embeddings of Hyperbolic Groups**

with Collin Bleak and Francesco Matucci.

*Journal of Combinatorial Algebra*5.2: 123–183- 2020
**On the Asynchronous Rational Group**

with James Hyde and Francesco Matucci.*Groups, Geometry, and Dynamics*13.4: 1271–1284.- 2020
**Embedding Right-Angled Artin Groups into Brin-Thompson Groups**

with Collin Bleak and Francesco Matucci.*Math. Proceedings of the Cambridge Philosophical Society*169.2: 225–229.- 2019
**Rearrangement Groups of Fractals**

with Bradley Forrest.*Transactions of the American Mathematical Society*372.7: 4509–4552.- 2017
**Some Undecidability Results for Asynchronous Transducers and the Brin-Thompson Group \(\boldsymbol{2V}\)**

with Collin Bleak.*Transactions of the American Mathematical Society*369.5: 3157–3172.- 2016
**Röver's Simple Group is of Type \(\boldsymbol{F_\infty}\)**

with Francesco Matucci.

*Publicacions Matemàtiques*60.2: 501–552.- 2015
**The Word Problem for Finitely Presented Quandles is Undecidable**

with Robert McGrail.

In*Logic, Language, Information, and Computation*, pp. 1–13. Springer.- 2015
**A Thompson Group for the Basilica**

with Bradley Forrest.*Groups, Geometry, and Dynamics*9.4: 975–1000.- 2014
**Implementation of a Solution to the Conjugacy Problem in Thompson's Group \(\boldsymbol{F}\)**

with Nabil Hossain, Francesco Matucci, and Robert McGrail.*ACM Communications in Computer Algebra*47.3/4: 120–121.- 2014
**CSPs and Connectedness: P/NP Dichotomy for Idempotent, Right Quasigroups**

with Benjamin Fish, Solomon Garber, Robert McGrail, and Japheth Wood.*Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on*, pp. 367–374. IEEE.- 2014
**Conjugacy and Dynamics in Thompson's Groups**

with Francesco Matucci.

*Geometriae Dedicata*169.1 (2014): 239–261.- 2013
**Deciding Conjugacy in Thompson's Group***F*in Linear Time

with Nabil Hossain, Francesco Matucci, and Robert McGrail.

*Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 15th International Symposium on*. IEEE.- 2010
**Iterated Monodromy for a Two-Dimensional Map**

with Sarah Koch.

*In the Tradition of Ahlfors–Bers, V, 1–12, Contemp. Math.*, 510, AMS.- 2005
**Thompson's Group \(\boldsymbol{F}\) is Maximally Nonconvex**

with Kai-Uwe Bux.*Geometric methods in group theory*, 131–146,*Contemp. Math.*, 372, AMS.- 2005
**Forest Diagrams for Elements of Thompson's Group \(\boldsymbol{F}\)**

with Kenneth Brown.*International Journal of Algebra and Computation*15, no. 5–6, 815–850.- 2004
**Thompson's group \(\boldsymbol{F}\)**

Ph.D. thesis, Cornell University, supervised by Kenneth Brown.

Slides for recent talks can be found at e.math.cornell.edu/people/belk/talks.htm.

**“Quasisymmetries of Finitely Ramified Fractals”**

September 2021

Topology & Geometric Group Theory Seminar, Cornell University

**“Tree Diagrams and Thompson's Groups”**

September 2021

Logic Seminar, Cornell University

**“Quasisymmetries of Finitely Ramified Julia Sets”**

March 2021

Analysis Seminar (via Zoom), St Andrews University

**“Finitely Presented Groups that Contain Q”**

June 2020

Topology and Geometric Group Theory Seminar (via Zoom),

Ohio State University

December 2019

*Groups and Geometry in the South East*,

University of Southampton

May 2019

*Workshop on Groups, Generalisations, and Applications*,

University of St Andrews

**“Twisted Brin–Thompson Groups”**

June 2020

Algebra Seminar (via Zoom), University of Milano–Bicocca

March 2020

Algebra & Combinatorics Afternoon, St Andrews University

January 2020

Algebra Seminar, Heriot–Watt University

**“Recognizing Topological Polynomials by Lifting Trees”**

February 2020

Geometry and Topology Seminar, University of Glasgow

**“On Embeddings into Infinite Simple Groups”**

January 2020

Mathematics Research Day, St Andrews University

**“The Tree Lifting Algorithm”**

November 2019

*Algorithms in Complex Dynamics and Mapping Class Groups*

ICERM, Brown University

**“Is Thompson's Group F Amenable?”**

February 2019

CIRCA Lunchtime Seminar, University of St Andrews

**“A Geometric Approach to the Twisted Rabbit Problem”**

December 2018

Complex Analysis, Dynamics, and Geometry Seminar,

University of Michigan

November 2018

Analysis Seminar, University of St Andrews

**“Rational Embeddings of Hyperbolic Groups”**

October 2018

Algebra Seminar, University of Aberdeen

October 2018

Pure Mathematics Colloquium, University of St Andrews

July 2018

Plenary Address, *Geometric Group Theory in Campinas*,

2018 ICM Satellite Conference, University of Campinas

March 2018

Geometry Topology Seminar, Georgia Institute of Technology

**“Embedding Right-Angled Artin Groups into Brin–Thompson Groups”**

March 2018

*52nd Spring Topology and Dynamical Systems Conference*

Auburn University

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

January 2017

Pure Mathematics Colloquium, University of St Andrews

**“Rearrangement Groups of Fractals”**

August 2016

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

April 2015

Geometry and Topology Seminar, Binghamton University

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

Finite Mathematics (F19, large lecture) | Real Analysis (S18, S12) |

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

Complex Analysis (S18) | Advanced Calculus (F17) |

Mathematical Modeling (F16) | Number Theory (S16) |

Measure Theory (S16, S11) | Topology (S15, F10) |

Differential Geometry (F14, F11) | Graduate Engineering Math (F07) |

Lower-Level Courses | |

First-Year Seminar (non-math, S17) | Physics II (with labs, S19, S09) |

Secret Codes (S15) | The Art of Secret Writing (S05, F04) |

Multivariable Calculus for Engineers (F21, large lecture) |
Engineering Mathematics II (F06, large lecture) |

Linear Algebra with ODE's (S17, F15, S14, F12) |
Calculus I (F21, S13, S12, F08, F05, Su04, S04, F03, S99) |

Calculus II (F17, F09) | Calculus III (F11) |

Vector Calculus (F16, S14) | Proofs & Fundamentals (F10) |

Problem-Solving Seminar (F09) | |

Tutorials (1-3 students) | |

Complex Dynamics (S18) | Geometric Group Theory (F17) |

Functional Analysis (F16) | Algorithms of Applied Math (F15) |

Representation Theory (F14) | Adv. Real Analysis (S17, S15, S14, S13) |

Algebraic Topology (F11) | Adv. Algebra (F16, S13, S10, F09, S09) |

Research Tutorial (F10) | Differential Geometry (F09) |

Complex Analysis (S09) |

All students at Bard College complete a year-long research project during their senior year. From 2009 to 2018, I supervised 24 such projects, covering a wide variety of topics. Projects marked with a star (*) are directly related to my research.

- 2018
- *Yuan Liu, “Graph Replacement Systems for Julia Sets of Quadratic Polynomials”
- *Rachel Nalecz, “An Implementation of the Solution to the Conjugacy Problem on Thompson’s Group \(V\)” (with Robert McGrail)
- 2017
- *Karuna Sangam, “Homeomorphisms of the Sierpiński Carpet”
- Avery Morris, “From Random to Organized: The Architecture of Neural Networks During Development”
- 2016
- *Cyril Kuhns, “Public-Key Cryptography with the Brin-Thompson Group \(2V\)” (with Robert McGrail)
- *Sarah Ghandour, “Random Walks on Thompson’s Group \(F\)”
- 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 \(F\)”

**College Service**

- • Bard College Council for Inclusive Excellence, Fall 2015–Spring 2017
- • Bard College Faculty Diversity Committee, Fall 2014–Spring 2017
- • Faculty Education and Oversight Committee for Bard College Berlin, Spring 2015–Spring 2018
- • Bard College Campus Facilities Committee, 2011–2013

**Mathematics Program Service**

- • Mathematics Program Chair, Fall 2017–Spring 2018
- • Search Committee for Mathematics Position, Fall 2017–Spring 2018
- • Conducted JMM Interviews for Mathematics Position, January 2016 and January 2018
- • Organized review sessions for the Mathematics Subject GRE (F11, F12, F17)
- • Putnam Exam Coordinator (F12, F16)
- • Co-organizer for three mathematics conferences at Bard College (F08, F09, F11)
- • Organizer, Bard College Mathematics/Physics/Computer Science Seminar, Fall 2009–Spring 2011
- • Organizer, Bard College Mathematics/Physics/Computer Science Seminar, Fall 2009–Spring 2011
- • Co-designed the web-based Mathematics Placement Diagnostic on Moodle for incoming students at Bard College, Fall 2008

**Outreach Activities**

- • Volunteer for the 2017 GAIM (Girls’ Adventures in Math) competition at Bard College
- • Proctor, 2016 AMC 8 middle school mathematics competition at Bard College
- • Speaker at the 2013, 2012, 2011, and 2010 Bard Summer Workshops for School Math Teachers
- • Gave a presentation on game theory for an audience of middle school students as part of the 2012 AMC 8 competition at Bard College
- • Visiting scholar at the 2011 Canada/USA Mathcamp at Reed College (gave talk and co-organized a 5-day minicourse)
- • Public lecture on fractal geometry for the Bard Lifetime Learning Institute, Fall 2011

**Refereeing**

I have refereed papers for the following journals:

- •
*Algebraic & Geometric Topology* - •
*Geometriae Dedicata* - •
*Groups, Geometry, and Dynamics* - •
*Israel Journal of Mathematics* - •
*Journal of Group Theory* - •
*Journal of Topology and Analysis* - •
*Transactions of the American Mathematical Society*

**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.