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Sergey Cherkis : Gravitational Instantons: the Tesseron Landscape

Since their introduction in Euclidean quantum gravity in mid-70�??s, hyperkaehler Gravitational Instantons (aka tesserons) found their use in string theory and in supersymmetric quantum field theory. Their classification was recently completed and now their parameter space is being explored. We propose a systematic program of realizing each of these spaces as a moduli space of monopoles: the monopolization program. Monopolization reveals the combinatorial and geometric structure of the parameter space of all these spaces, equips each space with various natural structures (tautological bundles, Dirac-type operators, etc), and connects different types of integrable systems associated to these gravitational instantons.

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