Nicholas W.M. Touikan

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1 Nicholas W.M. Touikan School of Mathematics & Statistics 4302 Herzberg Laboratories 1125 Colonel By Drive Ottawa, Ontario K1S 5B6 CANADA webpage: Field of research: I am a combinatorial and geometric group theorist. Education: Ph.D., Mathematics Adviser: Olga Kharlampovich B.Sc., Honours Mathematics Prizes and Distinctions: Sigma Xi Excellence in Undergraduate Research Award, 2004 McGill-Montreal Chapter of Sigma Xi. Research Fellowships: Positions: Fields Postdoctoral fellowship 08/ /2013 NSERC Postdoctoral fellowship (PDF) 09/ /2011 NSERC Alexander Graham Bell fellowship (CGS D2) 09/ /2009 Bourse de doctorat en recherche du FQRNT (B2) 05/ /2007 Bourse de maîtrise en recherche du FQRNT (B1) 09/ /2006 NSERC Undergraduate research award (USRA) 05/ /2003 Bourse d étude d été de l ISM 07/ /2002 Postdoctoral fellow, School of Mathematics and Statistics 01/ /2014 Fields postdoctoral fellow, School of Mathematics and Statistics 09/ /2013 1

2 Postdoctoral researcher in the ANR project Geometric, analytic 09/ /2012 and algorithmical aspects of groups, Université d Aix-Marseille NSERC postdoctoral fellow, Oxford Mathematical Institute 11/ /2011 NSERC postdoctoral fellow, CIRGET 09/ /2010 Teaching Experience: Teacher for 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 Organizer of the ISM inter-university graduate student seminar Representative for the department of Mathematics and Statistics in McGill s postgraduate student society. 2

3 Articles published in peer-reviewed journals: Bulitko s Lemma for acylindrical splittings Journal of Algebra, Volume 406 (2014), The fully residually F quotients of F x, y Groups, Geometry, and Dynamics, Volume 6 (2012), Issue 1, 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, The equation w(x, y) = u over free groups: an algebraic approach Journal of Group Theory, Volume 12 (2009), Issue 4, A Fast Algorithm for Stallings Folding Process International Journal of Algebra and Computation, Volume 16 (2006), Issue 6, Preprints: Isomorphisms using Dehn fillings: the splitting case (Joint with François Dahmani) Strong accessibility for finitely presented groups (submitted) (Joint with Lars Louder) Finding tracks in 2-complexes (submitted) 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 CMS Winter Meeting, Geometric Group Theory and Low Dimensional Topology Session, Ottawa (December ) On the isomorphism problem for relatively hyperbolic groups. Geometric and Asymptotic Group Theory with Applications (GAGTA 7), New York (May ) Hierarchical accessibility of finitely presented groups. (March ) NYGT Spring Seminar, New York 3

4 On the isomorphism problem for relatively hyperbolic groups CMS Winter Meeting, Geometric Group Theory Session, Montreal (December ) On the isomorphism problem for relatively hyperbolic groups. 70 th Algebra Days with focus on Geometric Group Theory, Ottawa (October ) Hierarchical accessibility of torsion free relatively hyperbolic groups. Infinite Groups, Lille (June ) Coarse Geometry of L accessibilité hiérarchique des groupes relativement hyperboliques (sans torsion). Seminaire de Topologie, Grenoble (June ) L accessibilité hiérarchique des groupes relativement hyperboliques (sans torsion). Séminaire Algèbre et Géométrie, Caen (June ) L accessibilité hiérarchique des groupes (relativement) hyperboliques. Séminaire de géométrie et dynamique, Lyon (April ) La géométrie des équations quadratiques sur les mots. Séminaire ERNEST Dynamique, Arithmétique et Combinatoire, Marseille (March ) La meilleure démonstration de Groupe de travail ACRO au LIF, Marseille (March ) La détection des scindements dans les groupes. Le séminaire Algèbre, Dynamique et Topologie, Marseille (March ) Accessibilité hiéarchique des groupes relativement hyperboliques. Le séminaire Teich, Marseille (December ) Théorie géométrique des groupes: les groupes hyperboliques. Groupe de travail ACRO au LIF, Marseille (December ) Limit groups are not conjugately residually free, but towers are. Interaction between Model Theory and Geometric Group Theory, Marseille (November ) Limit groups are not conjugately residually free. Barcelona (November ) 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 ) La détection des scindements dans les groupes. Séminaire GT3, Strasbourg (May ) La détection des scindements dans les groupes. Séminaire de Topologie, Grenoble (March ) Finding group splittings. Geometry and Topology Seminar, Warwick (February ) 4

5 Rips machine. Junior Geometric Group Theory Seminar, Oxford (January 26, February ) Finding tracks in cell complexes. Topology Seminar, Oxford (November ) Finding tracks in cell complexes. Topics in Algorithmic and Geometric Group and Semigroup Theory, Montreal (August ) Delzant and Potyagailo s hierarchical accessibility. Junior Geometric Group Theory Seminar, Oxford (April ) Finding Grushko decompositions. Poincaré seminar, Oxford (April ) Finding Grushko decompositions. Impromptu Volcano mini-conference, Southampton (April ) Finding Grushko decompositions. University (April ) 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 ) The Solvability problem for quadratic equations over free groups is NP-complete. CMS Winter Meeting 2008, Geometric Group Theory Session, Ottawa (December ) On the coordinate groups irreducible systems of equations in two variables over free groups. Residually Free Week at McGill, McGill (November ) Quadratic Equations over Free groups are NP-complete. Montreal (September ) 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 ) The equation w(x,y)=u over free groups, an algebraic approach. Workshop on Asymptotic Group Theory and Cryptography in Ottawa, (December ) Two Variable Equations over Free Groups: a Postmodern Approach. Théorie Combinatoire des Groupes, algorithmique et cryptographie, CIRM (February ) A fast algorithm for Stallings folding process. Montreal Geometric & Combinatorial Group Theory Seminar, McGill ( October ) Commutativity is for wimps! Elements of Algebraic Geometry over Free groups. ISM Graduate Student Seminar, Montreal (September ) Two variable equations over free groups. Geometric and Asymptotic Group Theory with Applications, Manresa (September ) 5

6 A fast algorithm for Stallings folding process. Workshop on Geometric Methods in Group Theory, (August ) Undecidability: Disturbing Results. ISM Graduate Student Seminar, Montreal (November ) Undecidability: Disturbing Results. Graduate student Seminar, Carleton University (November ) A fast Algorithm for Stallings folding process. CUNY Algebra and Cryptography Seminar, CUNY (October ) 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

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