LOCALIZATION, STRING DUALITY AND MODULI SPACES
定域化、弦对偶性和模空间
基本信息
- 批准号:0705284
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2007
- 资助国家:美国
- 起止时间:2007-08-15 至 2011-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
AbstractAward: DMS-0705284Principal Investigator: Kefeng LiuModuli spaces have played fundamental roles in many subjects ofmathematics from geometry, topology, algebraic geometry, to numbertheory. String duality from string theory has motivated many deepmathematical results and theories. The principal investigatorproposes to have an intensive study on applying localization methodcombined with other newly developed geometric techniques to solvefundamental problems arisen from string duality about the geometryand topology of moduli spaces of Riemann surfaces and stable maps.There are several specific problems that we hope to solve under thesupport of the proposed research grant, these include the generalrecursion formulas for intersection numbers of general tautologicalclasses which include the Faber conjecture as special case, the Virasoro conjecture for general projective manifolds,the understanding of topology, algebraic geometry of moduli spaces,and the computing of the holomorphic anomaly by using our geometricresults about moduli spaces.The interactions of mathematics and physics have motivated many fundamental advances in both disciplines.String Theory, as the most promising candidate for the grandunification of all fundamental forces in the nature, should includeall previous theories like the Yang-Mills and the Chern-Simonstheory. String duality which identifies different theories in stringtheory has produced many surprisingly beautiful mathematicalformulas about the geometry and topology of moduli spaces of Riemannsurfaces. The mathematical proofs of many of these conjecturalformulas depend crucially on localization techniques. This programwill not only help verify important physical theories, but alsoproduce beautiful and fundamental mathematics. In carrying out theproject we will also train several young students and post-doctors to conduct research inthese subjects through collaboration and lectures.
AbstractAward:DMS-0705284首席研究员:刘克峰模空间在从几何、拓扑、代数几何到数论的许多数学学科中起着基础性的作用。弦论的弦对偶性激发了许多深刻的数学结果和理论。主要研究者建议深入研究应用局部化方法结合其他新发展的几何技术来解决由弦对偶引起的关于黎曼曲面和稳定映射的模空间的几何和拓扑的基本问题。我们希望在拟议的研究基金的支持下解决几个具体问题,其中包括一般重言式类的交数的一般递推公式,包括作为特例的Faber猜想,一般射影流形的Virasoro猜想,拓扑学的理解,模空间的代数几何,数学和物理的相互作用推动了这两个学科的许多基本进展,弦论作为自然界中所有基本力的大统一的最有希望的候选者,应该包括所有以前的理论,如Yang-Mills理论和Chern-Simons理论。弦论中的弦对偶性是不同理论之间的区别,它产生了许多关于黎曼曲面模空间的几何和拓扑的令人惊讶的美丽的数学公式。这些数学公式的数学证明主要依赖于局部化技术。这一计划不仅有助于验证重要的物理理论,而且也产生美丽的和基本的数学。在实施该项目的过程中,我们还将培养一些年轻的学生和博士后,通过合作和讲座的方式进行这些学科的研究。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Kefeng Liu其他文献
Logarithmic vanishing theorems for effective q-ample divisors
有效 q 充足除数的对数消失定理
- DOI:
- 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
Kefeng Liu;Xueyuan Wan;Xiaokui Yang - 通讯作者:
Xiaokui Yang
GROUP TOPOLOGIES ON AUTOMORPHISM GROUPS OF HOMOGENEOUS STRUCTURES
齐次结构自同构群的群拓扑
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
Z. A. G. Hadernezhad;DE Javier;L. G. Onzalez;Matthias Aschenbrenner;Paul Balmer;Vyjayanthi Chari;Atsushi Ichino;Robert Lipshitz;Kefeng Liu;Dimitri Shlyakhtenko;Paul Yang;Ruixiang Zhang - 通讯作者:
Ruixiang Zhang
On orbifold elliptic genus
关于环褶椭圆属
- DOI:
10.1090/conm/310/05399 - 发表时间:
2001 - 期刊:
- 影响因子:0
- 作者:
C. Dong;Kefeng Liu;X. Ma - 通讯作者:
X. Ma
A ug 2 00 4 A MATHEMATICAL THEORY OF THE TOPOLOGICAL VERTEX
A ug 2 00 4 拓扑顶点的数学理论
- DOI:
- 发表时间:
2008 - 期刊:
- 影响因子:0
- 作者:
Li Jun;Chiu;Kefeng Liu;Jian Zhou - 通讯作者:
Jian Zhou
Genome-Wide Comparative Analyses of Pigmentation Genes in Four Fish Species Provides Insights on Fish Skin Color Patterning
对四种鱼类色素沉着基因的全基因组比较分析为鱼类肤色模式提供了见解
- DOI:
- 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
Lei Jia;Na Zhao;Xiaoxu He;K. Peng;Kefeng Liu;Bo Zhang - 通讯作者:
Bo Zhang
Kefeng Liu的其他文献
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{{ truncateString('Kefeng Liu', 18)}}的其他基金
Geometry of Deformation and Moduli Spaces of Complex Manifolds
复流形的变形几何和模空间
- 批准号:
1510216 - 财政年份:2015
- 资助金额:
-- - 项目类别:
Standard Grant
GEOMETRY AND TOPOLOGY OF THE MODULI SPACES OF RIEMANN SURFACES AND CALABI-YAU MANIFOLDS
黎曼曲面和卡拉比-丘流形模空间的几何和拓扑
- 批准号:
1007053 - 财政年份:2010
- 资助金额:
-- - 项目类别:
Continuing Grant
Geometry and Topology of Counting Curves in Projective Manifolds
射影流形中计数曲线的几何和拓扑
- 批准号:
0196544 - 财政年份:2001
- 资助金额:
-- - 项目类别:
Standard Grant
Geometry and Topology of Counting Curves in Projective Manifolds
射影流形中计数曲线的几何和拓扑
- 批准号:
0072182 - 财政年份:2000
- 资助金额:
-- - 项目类别:
Standard Grant
Applications of Modular Invariance in Geometry and Topology
模不变性在几何和拓扑中的应用
- 批准号:
9803234 - 财政年份:1998
- 资助金额:
-- - 项目类别:
Standard Grant
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