Representation theory of infinite-dimensional Lie superalgebras and related algebraic structures

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The proposal is concentrated around six interrelated topics: (1) Quantum Hamiltonian reduction and representation theory of superconformal algebras. (2) Admissible representations of affine superalgebras and elliptic functions.(3) Non-linear Lie conformal superalgebras. (4) Representation theory of finite simple Lie conformal superalgebras and Lie pseudoalgebras.(5) Representation theory of linearly compact Lie superalgebras and the models of electroweak and strong interactions. (6) Classification of infinite-dimensional primitive Lie superalgebras. This research is motivated to a large degree by recent and not so recent developments in Theoretical Physics, such as the Standard Model and the Conformal field theory. It is concerned with several directions of the supersymmetry theory. Several longstanding open problems from Conformal field theory have been and are being solved using the quantization of the classical Hamiltonian reduction. The unifying notion is the new notions of linear and non-linear Lie conformal superalgebras, which are being under intensive investigation.