Homogeneous manifolds. Einstein and Ricci soliton metrics. Ricci flow. Negative Ricci curvature. Prescribed Ricci curvature problem. Stability of Einstein metrics.

Complex, symplectic and G2-structures on Lie groups and homogeneous spaces. Geometric flows and their solitons.

Nilpotent Lie algebras. Variety of Lie algebras. Real geometric invariant theory.

Anosov diffeomorphisms on nilmanifolds.