Research interests:
- Algebraic geometry.
- D. Families, fibrations:
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(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).
- Nonassociative rings and algebras.
- B. Lie algebras and Lie superalgebras:
- (60) Lie (super)algebras associated with other structures (associative, Jordan, etc.)
- Topological groups, Lie groups.
- E. Lie groups:
- (25) Nilpotent and solvable Lie groups.
(30) Analysis on real and complex Lie groups.
- 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.
- Differential geometry.
- C. Global differential geometry:
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(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.
- 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 .