In this paper we present an overview of the direct relation between differential invariants of projective type for curves in flat semisimple homegenous spaces and PDEs of KdV type. We describe the progress in the proof of a conjectured Theorem stating that for any such space there are geometric evolutions of curves that induce completely integrable evolutions on their invariants of projective-t...

The 6 = 3 × 2 huge Lie algebra Ξ of all local and non local differential operators on a circle is applied to the standard Adler-Kostant-Symes (AKS) R-bracket sckeme. It is shown in particular that there exist three additional Lie structures, associated to three graded modified classical YangBaxter(GMCYB) equations. As we know from the standard case, these structures can be used to classify in a...

Since the x dependence of the axial-anomaly effect in inclusive polarized deep inelastic scattering is fixed, the transformation from the MS scheme to different factorization schemes are not arbitrary. If the quark spin distribution is demanded to be anomaly-free so that it does not evolve with Q and hard gluons contribute to the first moment of g1(x), then all the moments of coefficient and sp...

We adapt Hitchin's integrable systems to the case of a punctured curve. In the case of CP 1 and SL n-bundles, they are equivalent to systems studied by Garnier. The corresponding quantum systems were identified by B. Feigin, E. Frenkel and N. Reshetikhin with Gaudin systems. We give a formula for the higher Gaudin operators, using results of R. Goodman and N. Wallach on the center of the envelo...

By Phyllis Bottome. Faber & Faber, Ltd. Price 10s. 6d. net. This is the third appreciation of Adler published in England since his death at Aberdeen in August, 1937. It is written by a well-known novelist who, with her husband, was in close touch with Adler and his family for the last ten years of his life. It is the most intimate account yet available in English and gives many personal details...