Mathematical Sciences: Cohomology of the Mapping Class Group and the Moduli Space of Curves

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Professor John Harer plans to continue computing the homology of the moduli spaces and related spaces. He also intends to pursue further the connections between the Arbarello flag (and related flags) for a certain space of moduli and the Schubert cells of the Grassmannians of Hilbert space. This project brings together important objects from classical analysis, the moduli spaces of Riemann surfaces of genus g, with important objects from topology, n.dimensional manifolds and various associated groups. Results obtained can therefore be expected to interest a wide audience of mathematicians.