Research interests:

  1. Algebraic geometry.
      D. Families, fibrations:
        (20) Algebraic moduli problems, moduli of vector bundles. (21) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory).

  2. Nonassociative rings and algebras.
      B. Lie algebras and Lie superalgebras:
        (60) Lie (super)algebras associated with other structures (associative, Jordan, etc.)

  3. Topological groups, Lie groups.
      E. Lie groups:
        (25) Nilpotent and solvable Lie groups. (30) Analysis on real and complex Lie groups.

  4. Several complex variables and analytic spaces.
      G. Deformations of analytic structures:
        (05) Deformations of complex structures.
      J. Compact analytic spaces:
        (27) Compact Kaehler manifolds: generalizations, classification.

  5. Differential geometry.
      C. Global differential geometry:
        (10) G-structures. (15) General geometric structures on manifolds (almost complex, almost product structures, etc). (25) Special Riemannian manifolds (Einstein, Sasakian, etc). (26) Hyper-Kähler and quaternionic Kähler geometry, special geometry. (28) Twistor methods. (29) Issues of holonomy. (55) Hermitian and Kählerian manifolds.

  6. Global analysis, analysis on manifolds.
      E. Variational problems in infinite-dimensional spaces:
        (15) Application to extremal problems in several variables; Yang-Mills functionals , (20) Harmonic maps.
      G. Partial differential equations on manifolds; differential operators:
        (10) Index theory and fixed point theorems .