To attain and maintain a top world level in investigations of infinite groups by geometric methods, and spaces related to them.
Study of various notions of nonpositive curvature: CAT(0) spaces, Simplicial Non Positive Curvature and other forms of Combinatorial Nonpositive curvature.
Applications of nonpositive curvature tools to the study of special classes of groups: Coxeter groups, Artin groups, groups acting on buildings.
Topological study of various boundaries of groups and spaces: Gromov boundaries of hyperbolic groups, ending laminations spaces.
Introducing nonpositive curvature tools into the study of projective varieties: asphericity and hyperbolicity of ramified coverings.
