Maxime Bergeron, M. Robado, M. Scott. Écritures réduites de l'élément le plus long des groupes de Coxeter fini, McGill Undergraduate Mathematics Journal (The Delta-Epsilon), Fourth Issue (Winter 2010), pp.28-33. (Republished in the Bulletin de l’Association Mathématique du Québec, Vol. LII, no. 4, décembre 2012, pp.51-61.)
Abstract: Let G be a complex reductive linear algebraic group and let K be a maximal compact subgroup of G. Given a nilpotent group \Gamma generated by r elements, we consider the representation spaces Hom(\Gamma,G) and Hom(\Gamma,K) with the natural topology induced from an embedding into G^r and K^r respectively. The goal of this paper is to prove that there is a strong deformation retraction of Hom(\Gamma,G) onto Hom(\Gamma,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(\Gamma,G)//G onto Hom(\Gamma,K)/K.
Invariant Measures, Expanders and Property (T), essay for the McGill Ergodic Group Theory Day, December 2011.
Regular Weights and the Higman-Sims Graph, report on connections between constructions of the strongly regular Higman-Sims graph and regular weights on the corresponding association scheme yielding a new framework for the search of Type-II matrices, August 2011.
Gromov's Theorem on Groups of Polynomial Growth, report based on a seminar given by Mahmood Sohrabi at McGill University and the Lectures on Geometric Group Theory by Cornelia Drutu and Michael Kapovich, August 2010.