Alexander Kirillov

Subjects

Abelian categories, Algebraic geometry -- Cycles and subschemes -- Parametrization (Chow and Hilbert schemes), Algebraic geometry -- Families, fibrations -- Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Associative rings, Associative rings and algebras -- Representation theory of rings and algebras -- Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers, Associative rings and algebras -- Representation theory of rings and algebras -- Representation type (finite, tame, wild, etc.)., Associative rings and algebras -- Representation theory of rings and algebras -- Representations of quivers and partially ordered sets, Directed graphs, Graph theory, Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Representations, algebraic theory (weights), Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Root systems, Quantum field theory, Representations of graphs, Tensor products