Fields of interest:
Algebra, Metric geometry, and Low-dimensional topology. More specifically, my research explores geometric, analytic, combinatorial, and computational aspects of group theory. Examples are (i) the study of asymptotic invariants of groups: a group is considered as a metric space and geometric properties of the space are investigated such as the growth of balls or the isoperimetric inequalities; (ii) the study of C*-algebras associated with groups. Interactions with computer science and topological dynamics as well as probabilistic methods to study "random" group theoretical objects (groups, group elements, subgroups, etc.) are also my research topics.
- Isomorphism versus commensurability for a class of finitely presented groups, (G.N. Arzhantseva, J.-F. Lafont, A. Minasyan), Journal of Group Theory, (2014), no. 2, 361-378.
- Coarse non-amenability and coarse embeddings, (G.N. Arzhantseva, E. Guentner, J. Spakula), Geometric and Functional Analysis [GAFA], 22(1) (2012), 22-36.
- Coarse non-amenability and covers with small eigenvalues, (G.N. Arzhantseva and E. Guentner), Mathematische Annalen, 354(3) (2012), 863-870.
- Infinite groups with fixed point properties (with M.Bridson, T. Januszkiewicz, I. Leary, A. Minasyan, J. Swiatkowski),Geometry & Topology, 13 (2009), 1229--1263.
- Examples of random groups (with T. Delzant), (2008),preprint, submitted.
- The SQ-universality and residual properties of relatively hyperbolic groups, (with A. Minasyan and D. Osin), Journal of Algebra, 315(1) (2007), 165--177.
- Relatively hyperbolic groups are C*-simple (with A.Minasyan), Journal of Functional Analysis, 243(1) (2007), 345-351.
- Metrics on diagram groups and uniform embeddings in a Hilbert space, (with V.S. Guba, M.V. Sapir), Commentarii Mathematici Helvetici, 81(4) (2006), 911-929.