Nicholas Touikan


Postal service

Nicholas Touikan
Department of Mathematics and Statistics,
University of New Brunswick,
P.O. Box 4400,
Fredericton, NB, Canada
E3B 5A3




+1 506 458 7366

In person

My Office is Tilley Hall 407


I am an Associate Professor at the Department of Mathematics and Statistics of the University of New Brunswick. I dislike injustice.

Research Interest

My field of specialty is Geometric Group Theory, that is the study of groups as geometric objects. More specifically I study algorithmic problems in infinite discrete groups that exhibit some form of large scale non-positive curvature. I also use low dimensional topology to prove results about groups and group actions.


If you're an undergraduate student. The course website is hosted on D2L:

In Fall 2020, I'm also teaching Introduction to combinatorial and geometric group theory as part of the AARMS Advanced Courses program

Study with me

I am not accepting new graduate students at the moment.

Still an undergraduate student? Contact me to apply for an NSERC Undergraduate Research Award Experience!

Published or accepted articles

  1. Panel collapse and its applications (with Mark Hagen)(arxiv) Groups, Geometry, and Dynamics, Volume 13 (2019), Issue 4, 1285-1334. (journal, arXiv)
  2. Deciding Isomorphy using Dehn fillings: the splitting case (with François Dahmani), Inventiones Mathematicae, Volume 215 (2019), Issue 1, 81-169. (journal, arXiv, slides)
  3. On geodesic ray bundles in hyperbolic groups, Proceedings of the American Mathematical Society, Volume 146 (2018), 4165-4173. (journal, arXiv)
  4. Magnus pairs in, and free conjugacy separability of, limit groups (with Lars Louder), Geometria Dedicata, Volume 196 (2018), Issue 1, 187-201. (journal, arXiv, slides)
  5. Detecting geometric splittings in finitely presented groups, Transactions of the American Mathematical Society, Volume 370 (2018), 5635-5704. (journal, arXiv)
  6. Strong accessibility for finitely presented group (with Lars Louder), Geometry & Topology, Volume 21 (2017), 1805-1835. (journal, arXiv)
  7. Multipass automata and group word problems (with Tullio Ceccherini-Silberstein, Michel Coornaert, Francesca Fiorenzi, Paul E. Schupp), Theoretical Computer Science, Volume 600 (2015), 19-33. (journal, arxiv)
  8. On the one-endedness of graphs of groups, Pacific Journal of Mathematics, Volume 278 (2015), Issue 2, 463-478. (journal, arXiv, slides)
  9. Bulitko's Lemma for acylindrical splittings, Journal of Algebra, Volume 406 (2014), 251-271. (journal, arXiv)
  10. The fully residually F quotients of F*< x,y >, Groups, Geometry and Dynamics, Volume 6 (2012), Issue 1, 155-220. (journal, arXiv)
  11. The Solvability Problem for Quadratic Equations over Free Groups is NP-Complete (with Olga Kharlampovich, Igor Lysenok, and Alexei Myasnikov), Theory of Computing systems Volume 47 (2012), Issue 1, 250-258. (journal, arXiv, slides)
  12. The equation w(x, y) = u over free groups: an algebraic approach, Journal of group theory, Volume 12 (2009), Issue 4, 611-634. (journal, arXiv)
  13. A Fast Algorithm for Stallings' Folding Process, International Journal of Algebra and Computation, Volume 16 (2006), Issue 6, 1031-1045. (journal, arXiv)


  • On the quasi-isometric rigidity of graphs of surface groups (with Alex Taam)(arXiv, slides)

Work in progress

  • With Inna Bumagin, a paper on Makanin-Razborov diagrams for relatively hyperbolic is being written. A draft explaining what the limit groups are and how to obtain useful splittings is available upon request. (slides)