Bio

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.

Study with me

I am not accepting new graduate students at the moment.

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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)

Preprints

• On the quasi-isometric rigidity of graphs of surface groups (with Alex Taam)(arXiv, slides)
• Reducing the conjugacy problem for relatively hyperbolic automorphisms to peripheral components (with François Dahmani)(arXiv)