Nicholas W.M. Touikan School of Mathematics & Statistics 4302 Herzberg Laboratories 1125 Colonel By Drive Ottawa, Ontario K1S 5B6 CANADA email: nicholas.touikan@gmail.com webpage: http://people.math.carleton.ca/~ntouikan/ Field of research: I am a combinatorial and geometric group theorist. Education: Ph.D., Mathematics. 2004-2009 Adviser: Olga Kharlampovich B.Sc., Honours Mathematics 2000-2004 Prizes and Distinctions: Sigma Xi Excellence in Undergraduate Research Award, 2004 McGill-Montreal Chapter of Sigma Xi. Research Fellowships: Positions: Fields Postdoctoral fellowship 08/2012-08/2013 NSERC Postdoctoral fellowship (PDF) 09/2009-09/2011 NSERC Alexander Graham Bell fellowship (CGS D2) 09/2007-09/2009 Bourse de doctorat en recherche du FQRNT (B2) 05/2007-08/2007 Bourse de maîtrise en recherche du FQRNT (B1) 09/2004-04/2006 NSERC Undergraduate research award (USRA) 05/2003-08/2003 Bourse d étude d été de l ISM 07/2002-08/2002 Postdoctoral fellow, School of Mathematics and Statistics 01/2014-03/2014 Fields postdoctoral fellow, School of Mathematics and Statistics 09/2012-09/2013 1
Postdoctoral researcher in the ANR project Geometric, analytic 09/2011-09/2012 and algorithmical aspects of groups, Université d Aix-Marseille NSERC postdoctoral fellow, Oxford Mathematical Institute 11/2010-09/2011 NSERC postdoctoral fellow, CIRGET 09/2009-10/2010 Teaching Experience: Teacher for 201-103 VA (Calculus 1) Fall 2013 Vanier College Instructor for MATH 1007 (Calculus 1) Winter 2013 Instructor for MATH 1107 (Linear Algebra) Fall 2012 Postdoctoral co-supervisor of an ISM summer undergraduate Summer 2010 research internship. Université du Québec à Montréal Graduate mini-course: From Bass-Serre theory to JSJ decompositions Fall 2008 Graduate mini-course: Stable group actions on real trees Fall 2007 Teaching Assistant for MATH 140 (Calculus I) Fall 2006 Teaching Assistant for MATH 141 (Calculus II) Winter 2005 Teaching Assistant for MATH 235 (Basic Abstract Algebra) Fall 2005 Conferences Organized: Co-organizer of the first two workshops of the CRM Thematic Semester Summer 2010 in Geometric, Combinatorial and Computational Group theory. Miscellaneous Academic Activities: Reviewer for MathSciNet. Referee for peer-reviewed journals. VP Finance of the Postdoctoral Association (CUPA) 2013 Member of the Mathematics and Statistics house committee. 2008-2009 Organizer of the ISM inter-university graduate student seminar. 2007-2008 Representative for the department of Mathematics and Statistics 2006-2007 in McGill s postgraduate student society. 2
Articles published in peer-reviewed journals: Bulitko s Lemma for acylindrical splittings Journal of Algebra, Volume 406 (2014), 251-271. The fully residually F quotients of F x, y Groups, Geometry, and Dynamics, Volume 6 (2012), Issue 1, 155-220. The Solvability Problem for Quadratic Equations over Free Groups is NP-Complete (Joint with Igor Lysenok, Olga Kharlampovich, and Alexei Miasnikov) Theory of Computing systems, Volume 47 (2010), Issue 1, 250-258. The equation w(x, y) = u over free groups: an algebraic approach Journal of Group Theory, Volume 12 (2009), Issue 4, 611-634. A Fast Algorithm for Stallings Folding Process International Journal of Algebra and Computation, Volume 16 (2006), Issue 6, 1031-1045. Preprints: Isomorphisms using Dehn fillings: the splitting case (Joint with François Dahmani) http://arxiv.org/abs/1311.3937 Strong accessibility for finitely presented groups (submitted) (Joint with Lars Louder) http://arxiv.org/abs/1302.5451 Finding tracks in 2-complexes (submitted) http://arxiv.org/abs/0906.3902 Articles in preparation (working titles): On the one endedness of graphs of groups Limit groups for relatively hyperbolic groups (Joint with Inna Bumagin) Limit groups are not conjugately residually free (and some positive results as well) (Joint with Lars Louder) Presentations: Strong accessibility of finitely presented groups. 2013 CMS Winter Meeting, Geometric Group Theory and Low Dimensional Topology Session, Ottawa (December 7 2013.) On the isomorphism problem for relatively hyperbolic groups. Geometric and Asymptotic Group Theory with Applications (GAGTA 7), New York (May 29 2013.) Hierarchical accessibility of finitely presented groups. (March 8 2013.) NYGT Spring Seminar, New York 3
On the isomorphism problem for relatively hyperbolic groups. 2012 CMS Winter Meeting, Geometric Group Theory Session, Montreal (December 9 2012.) On the isomorphism problem for relatively hyperbolic groups. 70 th Algebra Days with focus on Geometric Group Theory, Ottawa (October 21 2012.) Hierarchical accessibility of torsion free relatively hyperbolic groups. Infinite Groups, Lille (June 22 2012.) Coarse Geometry of L accessibilité hiérarchique des groupes relativement hyperboliques (sans torsion). Seminaire de Topologie, Grenoble (June 13 2012.) L accessibilité hiérarchique des groupes relativement hyperboliques (sans torsion). Séminaire Algèbre et Géométrie, Caen (June 12 2012.) L accessibilité hiérarchique des groupes (relativement) hyperboliques. Séminaire de géométrie et dynamique, Lyon (April 18 2012.) La géométrie des équations quadratiques sur les mots. Séminaire ERNEST Dynamique, Arithmétique et Combinatoire, Marseille (March 13 2012.) La meilleure démonstration de 2011. Groupe de travail ACRO au LIF, Marseille (March 12 2012.) La détection des scindements dans les groupes. Le séminaire Algèbre, Dynamique et Topologie, Marseille (March 5 2012.) Accessibilité hiéarchique des groupes relativement hyperboliques. Le séminaire Teich, Marseille (December 9 2011.) Théorie géométrique des groupes: les groupes hyperboliques. Groupe de travail ACRO au LIF, Marseille (December 5 2011.) Limit groups are not conjugately residually free, but towers are. Interaction between Model Theory and Geometric Group Theory, Marseille (November 22 2011.) Limit groups are not conjugately residually free. Barcelona (November 8 2011.) Seminari Teoria de Grups UAB-UPC, L algorithmique des groupes (une introduction). Groupe de travail ACRO au LIF, Marseille (24 October 2011.) Conjugacy separability in limit groups. Pure Mathematics Colloquium, Southampton (May 13 2011.) La détection des scindements dans les groupes. Séminaire GT3, Strasbourg (May 2 2011.) La détection des scindements dans les groupes. Séminaire de Topologie, Grenoble (March 11 2011.) Finding group splittings. Geometry and Topology Seminar, Warwick (February 15 2010.) 4
Rips machine. Junior Geometric Group Theory Seminar, Oxford (January 26, February 2 2011.) Finding tracks in cell complexes. Topology Seminar, Oxford (November 22 2010.) Finding tracks in cell complexes. Topics in Algorithmic and Geometric Group and Semigroup Theory, Montreal (August 24 2010.) Delzant and Potyagailo s hierarchical accessibility. Junior Geometric Group Theory Seminar, Oxford (April 26 2010.) Finding Grushko decompositions. Poincaré seminar, Oxford (April 23 2010.) Finding Grushko decompositions. Impromptu Volcano mini-conference, Southampton (April 21 2010.) Finding Grushko decompositions. University (April 15 2010.) Pure Mathematics Postgraduate Conference, Newcastle Stable commutator length is rational in free groups. CIRGET Junior, 2009.) UQÀM (December 3 The Solvability problem for quadratic equations over free groups is NP-complete. Geometric and Asymptotic Group Theory with Applications, Hoboken (March 11 2009.) The Solvability problem for quadratic equations over free groups is NP-complete. CMS Winter Meeting 2008, Geometric Group Theory Session, Ottawa (December 6 2008.) On the coordinate groups irreducible systems of equations in two variables over free groups. Residually Free Week at McGill, McGill (November 6 2008.) Quadratic Equations over Free groups are NP-complete. Montreal (September 24 2008.) ISM Graduate Student Seminar, Quadratic equations over free groups are in NP. Workshop Actions on Trees, Non-Archimedean Words, and Asymptotic Cones, Saint-Sauveur (December 20 2007.) The equation w(x,y)=u over free groups, an algebraic approach. Workshop on Asymptotic Group Theory and Cryptography in Ottawa, (December 14 2007.) Two Variable Equations over Free Groups: a Postmodern Approach. Théorie Combinatoire des Groupes, algorithmique et cryptographie, CIRM (February 27 2007.) A fast algorithm for Stallings folding process. Montreal Geometric & Combinatorial Group Theory Seminar, McGill ( October 18 2006.) Commutativity is for wimps! Elements of Algebraic Geometry over Free groups. ISM Graduate Student Seminar, Montreal (September 27 2006.) Two variable equations over free groups. Geometric and Asymptotic Group Theory with Applications, Manresa (September 2 2006.) 5
A fast algorithm for Stallings folding process. Workshop on Geometric Methods in Group Theory, (August 18 2006.) Undecidability: Disturbing Results. ISM Graduate Student Seminar, Montreal (November 16 2005.) Undecidability: Disturbing Results. Graduate student Seminar, Carleton University (November 10 2005.) A fast Algorithm for Stallings folding process. CUNY Algebra and Cryptography Seminar, CUNY (October 28 2005.) Personal: I am the spouse of Charlène Rochefort-Allie and we have a daughter, Simone. Here are some other facts. Year of birth: 1981 Citizenship: Canadian Languages: Native speaker of English and French, basic knowledge of Cantonese and Mandarin. Erdös-Bacon number: 7 6