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报告题目:
2014清华大学陈省身讲座
 报告人:
Nigel Hitchin
牛津大学教授
英国皇家科学院院士
美国数学学会会员
报告时间:
2014-10-20 16:30
报告地点:
清华大学近春园西楼三层报告厅
主办单位:
数学科学中心
  简介:
为了表彰陈省身教授在微分几何领域的基础性贡献,清华大学数学科学中心于2011年设立清华大学陈省身讲座。该奖将颁给在几何领域做出杰出贡献的个人。获奖者将受邀来清华大学发表演讲,并接受证书以及奖金。
 
2014清华大学陈省身讲座
报告人:Nigel Hitchin,牛津大学
时间:16:30-17:30,2014年10月20日(周一),24日(周五)
地点:清华大学近春园西楼三层报告厅
 
讲座摘要:
Nigel Hitchin教授是近三十年来微分几何领域的领军人物。Nigel Hitchin教授在微分几何、代数几何和数学物理的研究中作出了开创性研究工作,开拓了新的研究方向,引发了许多后续的研究工作。
Nigel Hitchin教授的研究成果众多,1987年,他与三位物理学家合作率先建立了Hyper- Kähler流形及与超弦理论之间的深刻联系。在这个工作中,他奠定了过去25年间Hyper- Kähler几何研究的数学基础。
基于对Yang-Mills理论和Higgs理论工作,Nigel Hitchin教授发现了著名的Hitchin系统,其中一个例子就是Higgs丛。这个理论建立起来的第一个15年间的主要发展是代数几何中Hitchin系统的解空间。基于Hitchin系统基础性的性质,其成为代数数论和表示论的基本工具。
近来, 在Nigel Hitchin教授对Higgs丛的分析中,hyper-Kähler几何有发挥了重要作用。
 
报告人简介
Nigel Hitchin是英国数学家,牛津大学萨维尔几何学讲座教授,其研究领域包括微分几何、代数几何和数学物理。
Hitchin教授的著名发现包括:Hitchin可积系统、Hitchin-Thorpe不等式、HitchenTeichmüller空间上的射影平坦连接、Hitchen自对偶不等式、Atiyah-Hitchin单极度量、Atiyah-Hitchin-Singer定理、瞬子的ADHM结构(Atiyah、Drinfeld、HitchinManin共同完成)以及Hyperkähler系数(Hitchin、Karlhede、LindströmRocek共同完成)。
在他的一篇关于广义卡拉比-丘流形文章中,Hitchin教授介绍了广义复流形的概念,提供了包括泊松流形、辛流形、复流形等在内的单一结构。这些研究在几何图形通量紧化弦理论以及拓扑弦理论方面有广泛应用。
Hitchin教授的职业生涯中,他已指导过近30名研究生,包括Simon Donaldson(与Atiyah教授共同指导)。同时,他还担任杂志Mathematische Annalen的主编。
1991年,Hitchin当选英国皇家科学院院士,并于1998年当选牛津大学耶稣学院荣誉会员,此外,他还是1990年的高级贝里克奖,2000年的西尔维斯特奖及2002年波利亚奖获得者。2012年,他当选为美国数学学会会员。
 
2014 Tsinghua University Shiing-Shen Chern Distinguished Lecture
Speaker: Nigel Hitchin
Professor of University of Oxford
Fellow of the Royal Society
Fellow of the American Mathematical Society
 
Lecture 1: Higgs bundles – a survey
Time: 16:30-17:30, Oct. 20 (Mon.)
Tea break: 16:00-16:30
 
Lecture 2: Higgs bundles for diffeomorphism groups
Time: 16:30-17:30, Oct. 24 (Fri.)
Tea break: 16:00-16:30
Place: Lecture Hall, Floor 3, Jin Chun Yuan West Building, Tsinghua University
 
Abstract:
Professor Nigel Hitchin is a leading figure in differential geometry in the past thirty years. He is particularly well known for his originality and creativity. His ability to identify links among different research paradigms open new research directions for many to follow.
Among his numerous research accomplishments, in 1987 and in collaboration with three physicists, he articulated the subject of hyper-Kähler manifolds and its deep relation with super-string theory. Through this piece of work, he lays the mathematical foundation for the research of hyper-Kähler geometry in the past quarter century. It serves as a key impetus to inspire the development of geometry of special holonomy.
Based on his work on Yang-Mills Theory and Higgs' Monopoly Theory, Prof Hitchin discovered what is now known as Hitchin system. One example is the Higgs Bundle. While the development of this theory in its first fifteen years was mainly within the realm of integrable, due to its fundamental nature it has become a key tool in algebraic number theory and representation theory.
In his latest analysis of Higgs bundles, hyper-Kähler geometry emerges again.
 
Introduction of Speaker
Nigel Hitchin FRS is a British mathematician, Savilian Professor of Geometry, University of Oxford, working in the fields of differential geometry, algebraic geometry, and mathematical physics.
Amongst his notable discoveries are the Hitchin integrable system, the Hitchin–Thorpe inequality, Hitchin's projectively flat connection over Teichmüller space, Hitchin's self-duality equations, the Atiyah–Hitchin monopole metric, the Atiyah–Hitchin–Singer theorem, the ADHM construction of instantons (of Atiyah, Drinfeld, Hitchin, and Manin), and the Hyperkähler quotient (of Hitchin, Karlhede, Lindström and Rocek).
In his article on generalized Calabi–Yau manifolds, he introduced the notion of generalized complex manifolds, providing a single structure that incorporates, as examples, Poisson manifolds, symplectic manifolds and complex manifolds. These have found wide applications as the geometries of flux compactifications in string theory and also in topological string theory.
In the span of his career, Hitchin has supervised nearly thirty research students, including Simon Donaldson (part-supervised with Atiyah).
NIgel Hitchin is managing editor of the journal Mathematische Annalen.
In 1991 he was elected a Fellow of the Royal Society. Hitchin was elected as an Honorary Fellow of Oxford's Jesus College in 1998, and the Senior Berwick Prize (1990), the Sylvester Medal (2000) and the Pólya Prize (2002) have been awarded to him in honour of his far-reaching work. In 2012 he became a fellow of the American Mathematical Society.
 
Source: http://en.wikipedia.org/wiki/Nigel_Hitchin
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