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Chiu-Chu Melissa Liu

  1. Localization in Gromov-Witten Theory and Orbifold Gromov-Witten Theory.

    Втр, 07/26/2011 - 15:01 — SomNambul
    Authors: Chiu-Chu Melissa Liu
    Subjects: Algebraic Geometry
    Abstract

    In this expository article, we explain how to use localization to compute
    Gromov-Witten invariants of smooth toric varieties and orbifold Gromov-Witten
    invariants of smooth toric Deligne-Mumford stacks.

  2. Lectures on the ELSV formula.

    Ср, 04/07/2010 - 15:01 — SomNambul
    Authors: Chiu-Chu Melissa Liu
    Subjects: Algebraic Geometry
    Abstract

    The ELSV formula, first proved by Ekedahl, Lando, Shapiro, and Vainshtein,
    relates Hurwitz numbers to Hodge integrals. Graber and Vakil gave another proof
    of the ELSV formula by virtual localization on moduli spaces of stable maps to
    the projective line, and also explained how to simplify their proof using
    moduli spaces of relative stable maps to the projective line relative to a
    point. In this expository article, we explain what the ELSV formula is and how
    to prove it by virtual localization on moduli spaces of relative stable maps,
    following Graber-Vakil.

  3. The Coherent-Constructible Correspondence for Toric Orbifolds.

    Ср, 11/25/2009 - 16:01 — SomNambul
    Authors: Chiu-Chu Melissa Liu, Bohan Fang, David Treumann, Eric Zaslow
    Subjects: Algebraic Geometry
    Abstract

    This is a follow-up paper to \cite{FLTZ}. We extend the
    coherent-constructible correspondence of \cite{FLTZ} to include toric
    orbifolds. A toric orbifold $\cX_\bSi$ is described by a "stacky fan" $\bSi$
    lying in a real vector space $N_\bR,$ following Borisov-Chen-Smith \cite{BCS}.

  4. Orientability in Yang-Mills Theory over Nonorientable Surfaces.

    Ср, 09/02/2009 - 12:02 — SomNambul
    Authors: Nan-Kuo Ho, Chiu-Chu Melissa Liu, Daniel A. Ramras
    Subjects: Symplectic Geometry
    Abstract

    In arXiv:math/0605587, the first two authors have constructed a
    gauge-equivariant Morse stratification on the space of connections on a
    principal U(n)-bundle over a connected, closed, nonorientable surface. This
    space can be identified with the real locus of the space of connections on the
    pullback of this bundle over the orientable double cover of this nonorientable
    surface. In this context, the normal bundles to the Morse strata are real
    vector bundles.

  5. Orientability in Yang-Mills Theory over Nonorientable Surfaces.

    Ср, 09/02/2009 - 12:02 — SomNambul
    Authors: Nan-Kuo Ho, Chiu-Chu Melissa Liu, Daniel A. Ramras
    Subjects: Symplectic Geometry
    Abstract

    In arXiv:math/0605587, the first two authors have constructed a
    gauge-equivariant Morse stratification on the space of connections on a
    principal U(n)-bundle over a connected, closed, nonorientable surface. This
    space can be identified with the real locus of the space of connections on the
    pullback of this bundle over the orientable double cover of this nonorientable
    surface. In this context, the normal bundles to the Morse strata are real
    vector bundles.

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