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.
Complex Reductive Algebraic Groups, in case you find yourself wondering why a complex reductive algebraic group has a compact real form, December 2013.
Random Graphs, a somewhat detailed account of Erdős and Rényi's first paper on random graphs, April 2012.
Invariant Measures, Expanders and Property (T), essay for the McGill Ergodic Group Theory Day, December 2011.
Regular Weights and the Higman-Sims Graph, essay on connections between constructions of the Higman-Sims graph and regular weights on the corresponding association scheme, August 2011.
Gromov's Theorem on Groups of Polynomial Growth, essay 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.