## Current Developments in Mathematics |

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### Contents

One Dimensional Hyperbolic Systems of Conservation Laws | 1 |

Combinatorics symmetric functions and Hilbert schemes | 39 |

Periods of Limit Mixed Hodge Structures Richard Hain | 113 |

Copyright | |

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action AH(M algebra arithmetic theta bilipschitz boundary components bounded bundle coefficients coinvariant combinatorial compact compactification complex conjecture conservation laws construction Corollary corresponding curves cusps decomposition defined definition denote derived category diagram Eisenstein series Ending Lamination equation equivalent example fiber Figure filtration finite formula functor Garsia geodesic geometric limit given Gorenstein Hall-Littlewood polynomials hence Hilbert scheme holomorphic homeomorphic hyperbolic 3-manifolds ideal implies intersection cohomology invariant inversion irreducible isomorphism Kleinian groups Kostka-Foulkes polynomials Lemma linear locally symmetric locally symmetric space Macdonald polynomials manifold Math metric micro-support mixed Hodge structure module morphism nilpotent obtain orbit parabolic Q-subgroup parabolic rank partition pleated surfaces preprint proof Proposition proved quadratic quotient representation result Riemann ring Satake sequence sheaf sheaves solution stratum subgroup symmetric functions symmetric space Theorem theory topology torus tubes unipotent unique vanishing vector vertices weight Weyl group