The main results
include the N=1, N=2, N=3, and N=4 supersymmetric generalizations of the self-dual Yang-Mills equations in four dimensions and of the ADHM construction for instantons; a global operator formalism for free fields on higher-genus Riemann surfaces; derivation of the Virasoro action (non-commuting symmetries) on the KP hierarchy; constructing the representations for the sl(2), osp(1|2), and sl(2|1) affine Lie (super)algebras obtained by inverting the Hamiltonian reduction; the discovery of a hidden topological conformal symmetry in any non-critical string theory; the general construction of singular vectors of the N=2 superconformal algebra in two dimensions; the classification of degeneration patterns and of the embedding diagrams of N=2 Verma modules; the discovery of the equivalence of categories of highest-weight type representations of the N=2 superconformal algebra and of relaxed highest-weight type representations of the affine sl(2) algebra.