A formula equating open and closed Gromov-Witten invariants and its applications to mirror symmetry

We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of the form $X=\mathbb{P}(K_Y\oplus\mathcal{O}_Y)$, where $Y$ is a toric Fano manifold, are equal to certain 1-pointed closed Gromov-Witten invariants of $X$. As applications, we compute the mirror superpotentials for these manifolds. In particular, this gives a simple proof for the formula of the mirror superpotential for the Hirzebruch surface $\mathbb{F}_2$.Comment: v3: many minor changes, published in Pacific J. Math.; v2: 16 pages. Completely rewritten and improve

On the collapse of ideally elasto-plastic complex structures

Imperial Users onl

Does Misclassification of Equity Funds Exist? Evidence from Malaysia

Applying the style analysis developed by Sharpe (1988, 1992), this paper investigates the classification of equity funds in Malaysia. A methodology for creating purified mutual fund style indexes is used to verify existing classifications. The paper concludes that an improper classification of funds would not only cause mismatch between investors objectives and funds’ profile, it also affects the process of income smoothing in the lifecycle of investors. Besides estimating the possible economic impact due to misclassification, this study highlights the importance of a proper classification system of equity funds in Malaysian context and its implication towards investor’s protection.Mutual Fund Classification; Style Analysis; Investor’s Protection

SYZ mirror symmetry for toric Calabi-Yau manifolds

We investigate mirror symmetry for toric Calabi-Yau manifolds from the perspective of the SYZ conjecture. Starting with a non-toric special Lagrangian torus fibration on a toric Calabi-Yau manifold $X$, we construct a complex manifold $\check{X}$ using T-duality modified by quantum corrections. These corrections are encoded by Fourier transforms of generating functions of certain open Gromov-Witten invariants. We conjecture that this complex manifold $\check{X}$, which belongs to the Hori-Iqbal-Vafa mirror family, is inherently written in canonical flat coordinates. In particular, we obtain an enumerative meaning for the (inverse) mirror maps, and this gives a geometric reason for why their Taylor series expansions in terms of the K\"ahler parameters of $X$ have integral coefficients. Applying the results in \cite{Chan10} and \cite{LLW10}, we compute the open Gromov-Witten invariants in terms of local BPS invariants and give evidences of our conjecture for several 3-dimensional examples including K_{\proj^2} and K_{\proj^1\times\proj^1}.Comment: v3: final version, published in JDG 90 (2012), no. 2, 177-250. 71 pages, 14 figures; substantially revised and expande

Crash-Free Sequencing Strategies for Financial Development and Liberalization

This paper uses a stylized model of financial intermediation to characterize the exact circumstances along various paths of economic growth, financial development, and liberalization that can trigger a financial crisis. It shows how to avoid financial crises through proper sequencing of various financial development and liberalization measures. The results of the paper show that naive combinations of financial development and liberalization processes can give rise to financial crises. In some typical situations, in order to avoid a financial crisis, it is important that financial liberalization be accompanied by financial development, in the form of improvements in the financial sectorís efficiencies. In the case of fast growing economies, financial development becomes even more imperative. Copyright 2001, International Monetary Fund

Real Financial Integration among the East Asian Economies: A SURADF Panel Approach

To testify RIP, this study scrutinizes the mean-reversion behavior of bilateral real interest differentials (RIDs) in eight East Asian economies. We incorporate the ASEAN-5, South Korea and China (mainland) with the US and Japan taken as base countries. Four sub-samples within 1976-2004 are being considered to accentuate the effects of institutional changes and financial crises. To rectify the deficiency in extant univariate and panel tests, the newly proposed SURADF statistics by Breuer et al. (2002) is utilized. Overall, the findings are in favor of RIP such that RIDs are found mean-reverting (except China) and with faster adjustment, especially during the post-crisis era. Such outcome is in accord with the enhanced financial integration among the ASEAN-5 and South Korea with their major trading partners, suggesting that further economic cooperation and currency arrangements in the region are bright to preserve potential financial shocks. Conversely, the real financial integration among China-US and China-Japan are not yet empirically recognized notwithstanding the recent surge of capital flows into the mainland.Real Interest Differentials; SURADF Panel Unit Root Test; Half-life; Confidence Intervals; Financial Integration

ECG Round: A man with dizziness

published_or_final_versio

Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds

Let $X$ be a compact toric K\"ahler manifold with $-K_X$ nef. Let $L\subset X$ be a regular fiber of the moment map of the Hamiltonian torus action on $X$. Fukaya-Oh-Ohta-Ono defined open Gromov-Witten (GW) invariants of $X$ as virtual counts of holomorphic discs with Lagrangian boundary condition $L$. We prove a formula which equates such open GW invariants with closed GW invariants of certain $X$-bundles over $\mathbb{P}^1$ used to construct the Seidel representations for $X$. We apply this formula and degeneration techniques to explicitly calculate all these open GW invariants. This yields a formula for the disc potential of $X$, an enumerative meaning of mirror maps, and a description of the inverse of the ring isomorphism of Fukaya-Oh-Ohta-Ono.Comment: v4: 44 pages, 3 figures, minor modifications, final version to appear in DM

Gross fibrations, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds

For a toric Calabi-Yau (CY) orbifold $\mathcal{X}$ whose underlying toric variety is semi-projective, we construct and study a non-toric Lagrangian torus fibration on $\mathcal{X}$, which we call the Gross fibration. We apply the Strominger-Yau-Zaslow (SYZ) recipe to the Gross fibration of $\mathcal{X}$ to construct its mirror with the instanton corrections coming from genus 0 open orbifold Gromov-Witten (GW) invariants, which are virtual counts of holomorphic orbi-disks in $\mathcal{X}$ bounded by fibers of the Gross fibration. We explicitly evaluate all these invariants by first proving an open/closed equality and then employing the toric mirror theorem for suitable toric (partial) compactifications of $\mathcal{X}$. Our calculations are then applied to (1) prove a conjecture of Gross-Siebert on a relation between genus 0 open orbifold GW invariants and mirror maps of $\mathcal{X}$ -- this is called the open mirror theorem, which leads to an enumerative meaning of mirror maps, and (2) demonstrate how open (orbifold) GW invariants for toric CY orbifolds change under toric crepant resolutions -- an open analogue of Ruan's crepant resolution conjecture.Comment: v4: 65 pages, significantly shortened to avoid too much overlap with arXiv:1006.3830 and arXiv:1206.3994, to appear in JD