Geometry and Physics; Edinburgh, Scotland, UK

几何和物理；

• 批准号: 0908585
• 负责人: Lizhen Ji
• 金额: $ 1.75万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-05-01 至 2011-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908585&HistoricalAwards=false
• 关键词: Geometry; Physics; Edinburgh; Scotland; UK

Abstract:There have been interactions between mathematics and physics.One important example is the interaction between the theory of general relativity and Riemannian geometry. Other important examples include interactions between Yang-Mills gauge theory and connections on principal bundles, Higgs bosons and Higgs bundles (and Hitchin fibrations), string theory and algebraic geometry. Indeed, string theory has revolutionized the field of algebraic geometry, in particular, the enumerative algebraic geometry related to the moduli space of curves, and the Hitchin fibrations have also unexpectedly been used to prove the fundamental Lemma in the celebrated Langlands program in the theory of automorphic forms and representation theory.The conference ``Geometry and Physics: Atiyah80" will review the most recentdevelopments in such interactions with talks by leading experts from around the world.The marriage between mathematics and physics has been both long lastingand fruitful. Many important fields of modern mathematics have been directly motivated by applications in physics and mechanics,and physics can not be described accurately and effectivelywithout mathematics. Indeed, mathematics has played a crucial role in formulating properly and establishing rigorously physics theories, and in turn,developments in physics has provided mathematics with new motivations and unexpected problems. All these interactions inspired the famous physicist Eugene Wigner, a Nobel Laureate, to make the celebrated statement "The unreasonable effectiveness of mathematicsin natural sciences".This conference will also features a public event: The Higgs boson: what, why, how?

摘要：数学与物理之间一直存在着相互作用，广义相对论与黎曼几何之间的相互作用就是一个重要的例子。其他重要的例子包括杨-米尔斯规范理论与主丛、希格斯玻色子和希格斯丛（以及希钦纤维化）、弦理论和代数几何之间的相互作用。实际上，弦理论已经彻底改变了代数几何领域，特别是与曲线的模空间相关的枚举代数几何，希钦纤维化也意外地被用来证明自守形式理论和表示论中著名的朗兰兹纲领中的基本引理。Atiyah 80”将回顾这种互动的最新发展与来自世界各地的领先专家的谈话。数学和物理学之间的婚姻既持久又富有成果。 现代数学的许多重要领域都是由物理学和力学中的应用所直接推动的，而物理学的准确有效描述离不开数学。事实上，数学在正确地制定和建立严格的物理理论方面发挥了至关重要的作用，反过来，物理学的发展为数学提供了新的动力和意想不到的问题。所有这些相互作用激发了著名物理学家、诺贝尔奖获得者尤金维格纳（Eugene Wigner）发表了著名的声明“希格斯玻色子在自然科学中的不合理有效性”。本次会议还将举办一个公共活动：希格斯玻色子：什么，为什么，如何？