## Current Developments in MathematicsInternational Press, 2005 - Mathematics |

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### Contents

Complex geometry and supergeometry E DHoker | 1 |

String topology Background and present state | 41 |

The stability of matter and quantum electrodynam | 89 |

Copyright | |

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abelian variety absolutely irreducible amplitudes arXiv Barsotti-Tate basis bosons boundary bracket chain homotopy chain level channel chiral circles cobracket coefficients cohomology combinatorial complex components computation conjecture conjugacy classes corresponding curves defined deformation denote diagonal dimension Dirac operator E.H. Lieb electron embedded energy entropy equation equivalent equivariant factor finite flat group formula free loop space function G-torsor genus geometric Gr(k graph Hilbert Hilbert modular form Hochschild Holevo holographic algorithms holomorphic homology homotopy input invariant isomorphism Langlands Lemma Lett Lie algebra linear loop space magnetic field manifold matchgate Math matrix modular form moduli space nodes NP-complete Nucl operations orbital integrals output p-adic period matrix Phys planar planar graph polynomial prime problem proof quantized quantum quotient representation semisimple spin structures stability supergeometry superholomorphic supermoduli superstring supersymmetry surface symmetric signature tensor product theorem theory two-loop unramified vector weight zero