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Search Results: 1 - 10 of 59933 matches for " Jian Zhou "
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Localizations on Moduli Spaces and Free Field Realizations of Feynman Rules
Jian Zhou
Physics , 2003,
Abstract: We prove Iqbal's conjecture on the relationship between the free energy of closed string theory in local toric geometry and the Wess-Zumino-Witten model. This is achieved by first reformulating the calculations of the free energy by localization techniques in terms of suitable Feynman rule, then exploiting a realization of the Feynman rule by free bosons. We also use a formula of Hodge integrals conjectured by the author and proved jointly with Chiu-Chu Melissa Liu and Kefeng Liu.
A Conjecture on Hodge Integrals
Jian Zhou
Physics , 2003,
Abstract: We propose a conjectural formula expressing the generating series of some Hodge integrals in terms of representation theory of Kac-Moody algebras. Such generating series appear in calculations of Gromov-Witten invariants by localization techniques. It generalizes a formula conjectured by Mari\~no and Vafa, recently proved in joint work with Chiu-Chu Melissa Liu and Kefeng Liu. Some examples are presented.
Emergent Geometry of KP Hierarchy. II
Jian Zhou
Physics , 2015,
Abstract: We elaborate on a construction of quantum LG superpotential associated to a tau-function of the KP hierarchy in the case that resulting quantum spectral curve lies in the quantum two-torus. This construction is applied to Hurwitz numbers, one-legged topological vertex and resolved conifold with external D-brane to give a natural explanation of some earlier work on the relevant quantum curves.
Emergent Geometry of KP Hierarchy
Jian Zhou
Physics , 2015,
Abstract: We explain how to construct a quantum deformation of a spectral curve to a tau-function of the KP hierarchy. This construction is applied to Witten-Kontsevich tau-function to give a natural explanation of some earlier work. We also apply it to higher Weil-Petersson volumes and Witten's r-spin intersection numbers.
On Regularized Elliptic Genera of ALE Spaces
Jian Zhou
Physics , 2015,
Abstract: We define regularized elliptic genera of ALE space of type A by taking some regularized nonequivariant limits of their equivariant elliptic genera with respect to some torus actions. They turn out to be multiples of the elliptic genus of a K3 surface.
Fermionic Computations for Integrable Hierarchies
Jian Zhou
Physics , 2015,
Abstract: We present a unified fermionic approach to compute the tau-functions and the n-point functions of integrable hierarchies related to some infinite-dimensional Lie algebras and their representations.
Curve counting and instanton counting
Jian Zhou
Mathematics , 2003,
Abstract: We prove some combinatorial results required for the proof of the following conjecture of Nekrasov: The generating function of closed string invariants in local Calabi-Yau geometries obtained by appropriate fibrations of $A_N$ singularities over $P^1$ reproduce the generating function of equivariant $\hat{A}$-genera of moduli space of instants on $C^2$.
On computations of Hurwitz-Hodge integrals
Jian Zhou
Mathematics , 2007,
Abstract: We describe a method to compute Hurwitz-Hodge integrals.
Arithmetic McKay correspondence
Jian Zhou
Mathematics , 2008,
Abstract: We propose an arithmetic McKay correspondence which relates suitably defined zeta functions of some Deligne-Mumford stacks to the zeta functions of their crepant resolutions. Some examples are discussed.
Crepant Resolutions, Quivers and GW/NCDT Duality
Jian Zhou
Mathematics , 2009,
Abstract: We propose a conjecture that relates some local Gromov-Witten invariants of some crepant resolutions of Calabi-Yau 3-folds with isolated singularities with some Donaldson-Thomas type invariants of the moduli spaces of representations of some quivers with potentials.
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