Non-Kähler Hermitian geometry.  Compact and homogeneous case.  C-spaces.  

Homogeneous Rimannian 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.