Harmonic Superspace: New Directions

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We sketch recent applications of the harmonic superspace approach for off-shell formulations of $(4,4)$, $2D$ sigma models with torsion and for constructing super KdV hierarchies associated with "small" and "large" $N=4$ superconformal algebras.
12 pages, LaTeX, Talk given at the 10th International Conference on Problems Of Quantum Field Theory, Alushta (Crimea, Ukraine) 13-18 May 1996 (to be published in Proceedings)

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