Cornelia Druțu

Education and career

Awards

Publications

Selected contributions

• The quasi-isometry invariance of relative hyperbolicity; a characterization of relatively hyperbolic groups using geodesic triangles, similar to the one of hyperbolic groups.
• A classification of relatively hyperbolic groups up to quasi-isometry; the fact that a group with a quasi-isometric embedding in a relatively hyperbolic metric space, with image at infinite distance from any peripheral set, must be relatively hyperbolic.
• The non-distortion of horospheres in symmetric spaces of non-compact type and in Euclidean buildings, with constants depending only on the Weyl group.
• The quadratic filling for certain linear solvable groups.
• A construction of a 2-generated recursively presented group with continuously many non-homeomorphic asymptotic cones. Under the Continuum Hypothesis, a finitely generated group may have at most continuously many non-homeomorphic asymptotic cones, hence the result is sharp.
• A characterization of Kazhdan's property and of the Haagerup property using affine isometric actions on median spaces.
• A study of generalizations of Kazhdan's property for uniformly convex Banach spaces.
• A proof that random groups satisfy strengthened versions of Kazhdan's property for high enough density; a proof that for random groups the conformal dimension of the boundary is connected to the maximal value of p for which the groups have fixed point properties for isometric affine actions on spaces.

  Selected publications (in the order corresponding to the results above)

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• Published book