I am interested various aspects of birational geometry of complex Fano (or Fano-adjacent) varieties. To be precise, I am (or was) thinking about:

• K-stability and construction of moduli spaces for known families of Fano varieties,

• Equivariant birational geometry of Fano 3-folds: questions about birational rigidity and solidity,

• projectivized tangent bundles of Fanos and their properties (nefness, bigness, being a Mori Dream Space),

• the effective nonvanishing problem,

• algebraic contact manifolds and the LeBrun-Salamon conjecture.