I am Fellow and Tutor in Pure Mathematics at Exeter College, and University Lecturer in the Mathematical Institute, Oxford.
I completed my undergraduate and graduate studies in Pure Mathematics at the University of Iaşi, the oldest university in Romania. I studied for a doctorate and defended my PhD thesis in Mathematics in France, at the University of Paris-Sud (Paris XI), under the supervision of Pierre Pansu. After that, I have been “Maître de conférences” at the University of Lille 1, France. I also held a one-year visiting position at the Max -Planck-Institut für Mathematik in Bonn, and several short term visiting positions at the same institute, as well as at IHES (Institute des Hautes Études Scientifiques) in Paris. I have also defended in 2004 the second thesis in the French system (“Habilitation à diriger des recherches”).
In 2009 I received the Whitehead Prize of the London Mathematical Society.
My research interests lie in Geometric group theory, topology, and ergodic theory and its applications to number theory.
Part of my work relates to the program of classifying infinite finitely generated groups up to quasi-isometry. I have considered from this point of view semisimple Lie groups and their lattices, solvable Lie groups and their lattices, and relatively hyperbolic groups. Besides quasi-isometric rigidity problems, I have been interested in several quasi-isometry invariants among which the order of the Dehn function (related to the Word Problem), and the (Hilbert and Banach space) compression. The latter parameter measures how well can a finitely generated group with a word metric be embedded into a Hilbert or Banach space.
In the same area, I have worked lately on the relationship between, on one hand, actions of groups on different types of spaces (Lp-spaces, median spaces, spaces with measured walls) and, on the other hand, property (T) and its “opposite”, Haagerup property (or a-T-menability).
I studied also several other properties of groups, like the property of Rapid Decay (a property of the reduced C*-algebra of the group), and linearity.
The study of locally symmetric spaces constructed using arithmetic lattices led me to problems of Diophantine approximation and their relationship to the geometry of the above-mentioned spaces.
Through the work on relatively hyperbolic groups and metric spaces, I became interested in the geometry of the Mapping Class Groups and Teichmüller spaces. These spaces display a sort of relative hyperbolicity intermediate between the weak and the strong.