TOPOLOGICAL MIRROR SYMMETRY

拓扑镜像对称

• 批准号: EP/I020519/1
• 负责人: Minhyong Kim
• 金额: $ 20万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FI020519%2F1
• 关键词: TOPOLOGICAL; MIRROR; SYMMETRY

Dualities in theoretical physics are important tools to gain information on a physical model from its proposed duality with another typically more accessible physical theory. One such duality is mirror symmetry, which is a duality theory stemming from string theory. The mathematical implications of this duality are manifold. In the proposed project we are interested in relating these mathematical implications with ideas coming from number theory and representation theory. Namely, we propose to find patterns in the character tables of some finite matrix groups which explain this mirror symmetry from the perspective of Langlands duality. This latter is a vast program in modern number theory which in a special case implies Fermat's Last Theorem by the work of Andrew Wiles. In this proposal we are connecting via the study of the character tables of finite matrix groups, these two seemingly far dualities: mirror symmetry in string theory, and Langlands duality in number theory.

理论物理学中的对偶性是从物理模型提出的对偶性与另一种通常更容易理解的物理理论中获取有关物理模型信息的重要工具。其中一种对偶性是镜像对称，它是源于弦理论的对偶理论。这种二元性的数学含义是多方面的。在拟议的项目中，我们有兴趣将这些数学含义与来自数论和表示论的想法联系起来。也就是说，我们建议在一些有限矩阵群的特征表中寻找模式，从朗兰兹对偶性的角度解释这种镜像对称性。后者是现代数论中的一个庞大计划，在特殊情况下暗示了安德鲁·怀尔斯 (Andrew Wiles) 的费马大定理。在这个提案中，我们通过研究有限矩阵群的字符表，将这两个看似遥远的对偶性联系起来：弦论中的镜像对称性和数论中的朗兰兹对偶性。

项目成果

Prym varieties of spectral covers

光谱覆盖的 Prym 品种

• DOI: http://dx.10.2140/gt.2012.16.1609
• 发表时间: 2012
• 期刊: Geometry & Topology
• 影响因子: 2
• 作者: Hausel T

Positivity for Kac polynomials and DT-invariants of quivers

Kac 多项式和箭袋 DT 不变量的正性

• DOI: http://dx.10.4007/annals.2013.177.3.8
• 发表时间: 2013
• 期刊: Annals of Mathematics
• 影响因子: 4.9
• 作者: Hausel T

Arithmetic harmonic analysis on character and quiver varieties II

性状与箭袋品种的算术调和分析II

• DOI: http://dx.10.1016/j.aim.2012.10.009
• 发表时间: 2013
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Hausel T

Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces

两个曲面点的希尔伯特格式的反常过滤和权重过滤之间的交换

• DOI: http://dx.10.5427/jsing.2013.7c
• 发表时间: 2013
• 期刊: Journal of Singularities
• 影响因子: 0.4
• 作者: De Cataldo M