Geometry

Differential Geometry

Spaces of nonpositive curvature, Gromov hyperbolic spaces and groups, Asymptotic geometry, Geometry and analyis on metric spaces, Kaehler and hyperkaehler geometry.

Lie groups and Discrete Subgroups

Group actions on trees and products of trees, Kleinian groups, Bounded cohomology of locally compact groups, Applications in rigidity theory, Group actions on symmetric spaces, Ergodic theory on Lie groups.

Representation Theory

Representation theory of algebraic groups and Lie algebras, Cluster algebras, Cluster categories and their geometric models, Geometry of secant varieties, Representation theory of algebras and quivers.

Geometric Topology

Invariants of knots and links in three-manifolds, Knots in complex algebraic geometry (quasipositive knots) and contact geometry (Legendrian ribbons).

Symplectic Geometry

Gromov-Witten invariants, Floer homology, Hamiltonian dynamics, Lagrangian submanifolds, Pseudoholomorphic curves, ASD instantons, Moment maps, Symplectic vortex equations, Complex symplectic structures, Contact geometry, Symplectic field theory, Fukaya categories, Mirror symmetry, Seiberg-Witten and Donaldson invariants.