A growing importance of abstract algebraic and topological methods is a characteristic feature of mathematical physics of the second half of this century. The problems of uor proposal are directly related to this development. (1) Apply the theory of oper ads to the study of structures arising from (open or closed) string field theory and to the construction of higher products in the category of partial differential operators.(2) There is a significant recent interest in geometric structures modelled by p arabolic subgroups of semisimple Lie groups. We suggest to generalize the application of methods of representation theory of Lie groups, developed in the previous work of the applicants, to the study of the whole class of parabolicstructures, with a spec ial attention paid to invariant operators, generalized twistor objects and twistor correspondence.(3) Study geometric structures on vector bundles with applications to those structures which play a role in mathematical physics. Study the existence, class

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