Jim Belk Cornell University
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Curriculum Vitae

Contents
  1. Education
  2. Academic Positions
  3. Research Interests
  4. Publications and Preprints
  5. Recent Talks
  6. Courses and Tutorials
  7. Senior Projects
  8. Service and Professional Work

EDUCATION

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

ACADEMIC POSITIONS


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

RESEARCH INTERESTS

Main Research Areas
    Geometric Group Theory, Dynamical Systems

Other Research Interests
    Geometric topology, fractal geometry, automata theory, graph theory, discrete geometry.

PUBLICATIONS AND PREPRINTS

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.

RECENT TALKS

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

COURSES AND TUTORIALS

See www-groups.mcs.st-and.ac.uk/~jmb42/teaching.htm for course descriptions.
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)

SENIOR PROJECTS

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 \(F\)”

SERVICE AND PROFESSIONAL WORK

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.