Mathematical Sciences: Modular Cohomology and Nonlinear Index Problems

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Elliptic cohomology has made possible an analytic interpretation of part of complex cobordism in terms of nonlinear supersymmetric sigma-models. Morava intends to extend this interpretation to the whole of the complex cobordism functor by studying surfaces of arbitrary genus. He approaches this from three directions: (i) The Virasoro algebra and cobordism comodules (ii) Analytic vector bundles over local number rings (iii) The transfer operation on mapping-spaces. There are three technical devices which have already yielded him results: (i) Elliptic hyperbole (ii) Infinitesimal automorphisms of elliptic cohomology (iii) Chern classes of local line bundles.