Curriculum Vitae
ACADEMIC POSITIONS
Fall 2022 – Present
University of Glasgow
Lecturer, School of Mathematics & Statistics
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
EDUCATION
Cornell University
PhD Mathematics, August 2004
MS Mathematics, May 2002
Binghamton University
MA Mathematics, May 1999
BS Mathematics and Physics, May 1998
RESEARCH INTERESTS
Main Research Areas
Geometric Group Theory, Complex Dynamics
Other Research Interests
Symbolic Dynamics, C*-algebras, Geometric Topology, Fractal Geometry,
Quasiconformal Geometry, Automata Theory
PUBLICATIONS AND PREPRINTS
Click on the 
icon to download the corresponding manuscript.
- Boone–Higman embeddings of Aut(Fn) and mapping class groups of punctured surfaces
with Francesco Fournier-Facio, James Hyde, and Matthew C. B. Zaremsky.
Preprint (2025). arXiv:2503.21882. - Finite germ extensions
with James Hyde and Francesco Matucci.
Preprint (2024). arXiv:2407.03149. - Thurston's theorem and the Nielsen–Thurston classification via Teichmüller's theorem
with Dan Margalit and Rebecca R. Winarski.
Preprint (2023). arXiv:2309.06993. - Pseudo-F4 is isomorphic to F4
with Liam Stott.
Preprint (2023). arXiv:2303.16868. - Automorphisms of shift spaces and the Higman–Thompson groups: the two-sided case
with Collin Bleak, Peter Cameron, and Feyishayo Olukoya.
Preprint (2021). arXiv:2006.01466. - Stabilizers in Higman–Thompson groups
with James Hyde and Francesco Matucci.
Preprint (2021). arXiv:2104.05572. - Boone–Higman embeddings for contracting self-similar groups
with Francesco Matucci.
Preprint (2024). Accepted to Groups, Geometry, and Dynamics. arXiv:2405.10234. - Hyperbolic groups satisfy the Boone–Higman conjecture
with Collin Bleak, Francesco Matucci, and Matthew Zaremsky.
Preprint (2023). Accepted to Duke Mathematical Journal. arXiv:2309.06224. - Quasisymmetries of finitely ramified Julia sets
with Bradley Forrest.
Preprint (2023). Accepted to Mathematische Annalen. arXiv:2310.17442. - Progress around the Boone–Higman conjecture
with Collin Bleak, Francesco Matucci, and Matthew Zaremsky.
Preprint (2023). Accepted to EMS Surveys in Mathematical Sciences. arXiv:2306.16356. - A piecewise linear homeomorphism of the circle which is periodic under renormalization
with James Hyde and Justin Moore.
Preprint (2022). Accepted to Groups, Geometry, and Dynamics. arXiv:2211.05825. - 2025
- The maximality of T in Thompson's group V
with Collin Bleak, Martyn Quick, and Rachel Skipper.
Archiv der Mathematik 125: 1–7. - 2025
- Type systems and maximal subgroups of Thompson's group V
with Collin Bleak, Martyn Quick, and Rachel Skipper.
Transactions of the American Mathematical Society, Series B 12: 417–469. - 2025
- A short proof of Rubin's theorem
with Luna Elliott and Francesco Matucci.
Israel Journal of Mathematics 267: 157–169. - 2023
- Conjugator length in Thompson's groups
with Francesco Matucci.
Bulletin of the London Mathematical Society 55.2: 793–810. - 2022
- Recognizing topological polynomials by lifting trees
with Justin Lanier, Dan Margalit, and Rebecca R. Winarski.
Duke Mathematical Journal 171.17: 3401–3480. - 2022
- Embedding Q into a finitely presented group
with James Hyde and Francesco Matucci.
Bulletin of the American Mathematical Society 59: 561–567. - 2022
- Twisted Brin–Thompson groups
with Matthew C. B. Zaremsky.
Geometry & Topology 26.3: 1189–1223. - 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 \(\boldsymbol{\mathrm{F}_{\!\infty}}\)
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, WoLLIC 2015. Lecture Notes in Computer Science 9160. Springer, 1–13. - 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.
2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 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, Robert McGrail, and Francesco Matucci.
2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 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 S. Brown.
RESEARCH TALKS
Slides for recent talks can be found on my talks page.
“Boone–Higman Embeddings of Aut(Fn) and Mapping Class Groups of Punctured Surfaces”
September 2025
Al@Bicocca Flash Workshop (via Zoom),
University of Milan–Bicocca
May 2025
North British Geometric Group Theory Seminar, University of St Andrews
“Thurston's Theorem, Twisted Rabbits, and Trees”
July 2025
2025 Early Career Complex Dynamics Workshop,
Indiana University Bloomington
“Embeddings into Topological Full Groups”
June 2024
Analysis Seminar, University of Copenhagen
June 2023
Algebra, Geometry and C*-algebras,
International Centre for Mathematical Sciences, Edinburgh
“Boone–Higman for Hyperbolic Groups”
September 2023
GoTh Workshop, Otto-von-Guericke-Universität Magdeburg
“Finite Germ Extensions”
July 2023
Al@Bicocca Flash Workshop, University of Milan–Bicocca
April 2023
Groups and Topology, Lancaster University
“Quasisymmetry Groups of Finitely Ramified Fractals”
May 2023
Analysis Seminar, University of Glasgow
“Embeddings into Finitely Presented Simple Groups”
December 2022
Group Theory Seminar, ENS Paris
December 2022
Algebra Seminar, University of Milano–Bicocca
October 2022
Topology and Geometry Seminar, University of Glasgow
September 2022
Dame Kathleen Ollerenshaw Workshop: Modern Advances in Geometric Group Theory, University of Manchester
“Turing Machines, Automata, and the Brin–Thompson Group 2V”
September 2021
Logic Seminar, Cornell University
“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
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
“Dynamics and Decidability in Brin’s Group 2V”
May 2014
Workshop on the Extended Family of R. Thompson’s Groups,
University of St Andrews
“Thompson-Like Groups for Self-Similar Structures”
May 2014
Workshop on the Extended Family of R. Thompson’s Groups,
University of St Andrews
“Turing Machines, Automata, and the Brin–Thompson Group 2V”
November 2013
Algebra/Topology Seminar, SUNY Albany
October 2013
Oberseminar Gruppen und Geometrie, Bielefeld University
October 2013
Groupes de Travail de L'équipe Topologie Dynamique,
Paris–Sud University
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 Seminar, University of St Andrews
August 2013
Groups St Andrews 2013, University of St Andrews
“Symmetries of Julia Sets”
April 2013
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
Algebra and Topology Seminar, Binghamton University
“Conjugacy and Dynamics in Thompson's Groups”
October 2008
Topology/Geometry Seminar, Rutgers University
April 2007
Algebra Seminar, University of Virginia
April 2007
Topology Seminar, Cornell University
November 2006
Groups and Dynamics Seminar, Texas A&M University
“Braids Without Twists”
January 2008
AMS Session on Algebra and Group Theory,
2008 Joint Mathematics Meetings in San Diego, California
“Conjugacy in Thompson’s Group F”
November 2006
Mathematics Postdoc Colloquium, Texas A&M University
“Strand Diagrams, Configuration Spaces, and Associahedra”
March 2006
Groups and Dynamics Seminar, Texas A&M University
“Forest Diagrams for Elements of Thompson's Group F”
September 2005
Groups and Dynamics Seminar, Texas A&M University
October 2004
Topology Seminar, Binghamton University
October 2003
AMS Special Session on Geometric Group Theory,
2003 Fall Eastern Sectional Meeting at Binghamton University
October 2003
Topology Seminar, Cornell University
June 2003
International Conference on Group Theory, Gaeta, Italy
“Amenability and the Banach–Tarski Paradox”
February 2002
Olivetti Club, Cornell University
COURSES TAUGHT
See my teaching page for course descriptions.| Upper-Level Courses | |
|---|---|
| Algebraic & Geometric Topology (F22, F23, F24) |
Finite Mathematics (F19, co-taught) |
| Dynamical Systems (F15, F14, F12, S11, F08) |
Abstract Algebra (S13, S10, S09) |
| Real Analysis (S18, S12) | 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, S10, S09) |
| Secret Codes (S15) | The Art of Secret Writing (S05, F04) |
| Modeling with Calculus for the Life Sciences (S22, large lecture) |
Multivariable Calculus for Engineers (F21, 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) |
| Engineering Mathematics II (F06, large lecture) |
Problem-Solving Seminar (F09) |
| Groups, Transformations and Symmetries (S23, S24, S25) |
PHD STUDENTS
I have co-supervised one PhD student at the University of Milano–Bicocca.
- 2023
- *Davide Perego, “Rationality of Boundaries”
(with Francesco Matucci)
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
Service at the University of Glasgow
- • Organizer, Topology and Geometry Seminar, Fall 2022–Spring 2023
College Service at Bard
- • 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 at Bard
- • 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.