Tsung-Ju Lee

We give a Hodge-theoretic criterion for a Calabi--Yau variety to have finite Weil--Petersson distance on higher dimensional bases up to a set of codimension $\geq 2$. The main tool is variation of Hodge structures and variation of mixed Hodge structures. We also give a description on the codimension 2 locus for the moduli space of Calabi--Yau threefolds. We prove that the points lying on exactly one finite and one infinite divisor have infinite Weil--Petersson distance along angular slices. Finally, by giving a classification of the dominant term of the candidates of the Weil--Petersson potential, we prove that the points on the intersection of exact two infinite divisors have infinite distance measured by the metric induced from the dominant terms of the candidates of the Weil--Petersson potential.

Base (topology)

10.4310/mrl.2018.v25.n2.a14

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Citations (2)

Period domains for gravitational instantons

Transactions of the American Mathematical Society (2022)

Tsung-Ju Lee Yu-Shen Lin

Based on the uniformization theorems of gravitation instantons by Chen–Chen [Acta Math. 227 (2021), pp. 263–307], Chen–Viaclovsky [Gravitational instantons with quadratic volume growth, 2021], Collins–Jacob–Lin [Forum Math. Sigma (2021)], and Hein–Sun–Viaclovsky–Zhang [Gravitational instantons and del Pezzo surfaces], we prove that the period maps for the A L H ∗ \mathrm {ALH}^{\ast } , A L G \mathrm {ALG} , and A L G ∗ \mathrm {ALG}^{\ast } gravitational instantons are surjective. In particular, the period domains of these gravitational instantons are exactly their moduli spaces.

Instanton

10.1090/tran/8856

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A Hodge theoretic criterion for finite Weil--Petersson degenerations over a higher dimensional base

arXiv (Cornell University) (2016)

Tsung-Ju Lee

We give a Hodge-theoretic criterion for a Calabi--Yau variety to have finite Weil--Petersson distance on higher dimensional bases up to a set of codimension $\geq 2$. The main tool is variation of Hodge structures and variation of mixed Hodge structures. We also give a description on the codimension 2 locus for the moduli space of Calabi--Yau threefolds. We prove that the points lying on exactly one finite and one infinite divisor have infinite Weil--Petersson distance along angular slices. Finally, by giving a classification of the dominant term of the candidates of the Weil--Petersson potential, we prove that the points on the intersection of exact two infinite divisors have infinite distance measured by the metric induced from the dominant terms of the candidates of the Weil--Petersson potential.

Codimension

Base (topology)

10.48550/arxiv.1604.06914

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Tautological systems under the conifold transition on $G(2,4)$

Asian Journal of Mathematics (2019)

Tsung-Ju Lee Hui-Wen Lin

Via a natural degeneration of Grassmannian manifolds $G(k,n)$ to Gorenstein toric Fano varieties $P(k,n)$ with conifold singularities, we suggest an approach to study the relation between the tautological system on $G(k,n)$ and the extended GKZ system on the small resolution $\hat{P}(k,n)$ of $P(k,n)$. We carry out the simplest case $(k,n)=(2,4)$ to ensure its validity and show that the extended GKZ system can be regarded as a tautological system on $\hat{P}(2,4)$.

Conifold

10.4310/ajm.2019.v23.n3.a7

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On Calabi–Yau fractional complete intersections

Pure and Applied Mathematics Quarterly (2022)

Tsung-Ju Lee Bong H. Lian Shing–Tung Yau

Calabi–Yau manifold

10.4310/pamq.2022.v18.n1.a10

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Resource allocation and dynamic provisioning for Service-Oriented applications in cloud environment

Kuo‐Chan Huang Bo-Jyun Shen Tsung-Ju Lee Hsi‐Ya Chang Yuan-Hsin Tung

Cloud computing has caused a revolution in our way of using software. Software development and deployment based on the new models of Software as a Service (SaaS) and Service-Oriented Architecture (SOA) are expected to bring a lot of benefits for users. However, software developers and software service providers will have to address new challenging issues before such benefits can be realized. The issues mainly arise from two characteristics of service-based applications: software based on distributed service flows and online concurrent user access. This paper deals with one of the important issues concerning resource allocation and dynamic provisioning for the deployed services in a cloud environment. We propose a service deployment strategy based on the structural property of application service flows and a dynamic resource provisioning mechanism utilizing the estimation of future service requests. A series of experiments were conducted on the CloudSim platform to evaluate the proposed mechanisms. The experimental results indicate that the proposed methods significantly outperform the commonly used primitive approaches, achieving up to 79.9% performance improvement.

Provisioning

10.1109/cloudcom.2012.6427592

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Citations (11)

Twisted GKZ hypergeometric functions and relative homology

Mathematische Annalen (2024)

Tsung-Ju Lee Dingxin Zhang

Hypergeometric distribution

Homology

Zhàng

10.1007/s00208-024-03058-6

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Twisted GKZ hypergeometric functions and relative cohomology

arXiv (Cornell University) (2023)

Tsung-Ju Lee Dingxin Zhang

We investigate the GKZ $A$-hypergeometric $\mathscr{D}$-modules, introduced by Gel'fand, Kapranov, and Zelevinskii, arising from cyclic covers of toric varieties and find its Riemann--Hilbert partner. This extends our earlier results in arXiv:1902.01536.

Hypergeometric distribution

10.48550/arxiv.2302.08430

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Mirror duality between Calabi-Yau fractional complete intersections

arXiv (Cornell University) (2022)

Tsung-Ju Lee

This is an expanded version of the author's talk at the third annual meeting of International Consortium of Chinese Mathematicians held at USTC in December 2020. In this expository article, we give a survey on joint works with Hosono, Lian, and Yau in arXiv:2003.07148 and arXiv:2008.04039. We also carry out some explicit examples to illustrate our results in enumerative geometry which will appear in our forthcoming papers.

Duality (order theory)

Calabi–Yau manifold

Carry (investment)

10.48550/arxiv.2206.06571

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On a conjecture of Huang–Lian–Yau–Yu

Communications in Analysis and Geometry (2023)

Tsung-Ju Lee Bong H. Lian Dingxin Zhang

10.4310/cag.2023.v31.n6.a1

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