Nicholas Touikan

Contact

Postal service

Dr. Nicholas Touikan
Stevens Institute of Technology
Department of Mathematical Sciences
1 Castle Point Terrace
Hoboken, New Jersey
07030, USA

Email

nicholas.touikan@gmail.com

Telephone

+1 201 216 8596

In person

My Office is Kidde 229

Bio

I am currently a Teaching Associate Professor at the Department of Mathematical Sciences of the Stevens Institute of Technology. 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 and equations in discrete groups that have large scale non-positive curvature. I also study connections and analogies between group theory and low dimensional topology. I plan to apply this perspective that interweaves discrete geometry and computability to problems in computer and data science.

At Stevens I am also an active member of the Calculus Project, a research effort to determine how to effectively use new teaching technologies and promote reasoning based learning.

Published or accepted articles

  1. On geodesic ray bundles in hyperbolic groups, accepted by Proceedings of the American Mathematical Society. (arXiv)
  2. Magnus pairs in, and free conjugacy separability of, limit groups (with Lars Louder), Geometria Dedicata, Published online 06 January 2018. (journal, arXiv, slides)
  3. Detecting geometric splittings in finitely presented groups, Transactions of the American Mathematical Society, Published online 22 March, 2018. (journal, arXiv)
  4. Strong accessibility for finitely presented group (with Lars Louder), Geometry & Topology, Volume 21 (2017), 1805-1835. (journal, arXiv)
  5. 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)
  6. On the one-endedness of graphs of groups, Pacific Journal of Mathematics, Volume 278 (2015), Issue 2, 463-478. (journal, arXiv, slides)
  7. Bulitko's Lemma for acylindrical splittings, Journal of Algebra, Volume 406 (2014), 251-271. (journal, arXiv)
  8. The fully residually F quotients of F*< x,y >, Groups, Geometry and Dynamics, Volume 6 (2012), Issue 1, 155-220. (journal, arXiv)
  9. 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)
  10. 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)
  11. A Fast Algorithm for Stallings' Folding Process, International Journal of Algebra and Computation, Volume 16 (2006), Issue 6, 1031-1045. (journal, arXiv)

Preprints

  • Deciding Isomorphy using Dehn fillings: the splitting case (with François Dahmani) (arXiv, slides)
  • Panel collapse and its applications (with Mark Hagen)(arxiv)

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)
  • With Alex Taam, a paper showing quasi-isometric rigidity of certain graphs closed surface groups with cyclic edge groups. (slides)