Representation Theory and applications to Combinatorics, Geometry and Quantum Physics

表示理论及其在组合学、几何和量子物理中的应用

• 批准号: 1358171
• 负责人: Pavel Etingof
• 金额: $ 3万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-12-01 至 2015-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1358171&HistoricalAwards=false
• 关键词: Representation; Theory; applications; Combinatorics; Geometry

The conference 'Representation Theory and Applications to Combinatorics, Geometry and Quantum Physics' will be held on December 13 through 19, 2013, at the Independent University of Moscow in Russia. It will be a major gathering of the leading mathematicians and young scholars whose work fits in the realm of representation theory. The conference has a broad scope and it aims to present some of the most important recent developments and techniques in this field, in particular the rich web of interconnections between representation theory, combinatorics, geometry, and physics, which has emerged in recent years and has greatly helped to advance each of these fields. The topics to be covered in the conference include algebraic groups, geometric representation theory, vertex algebras, infinite dimensional Lie algebras, combinatorics of plane partitions, conformal field theory and enumerative algebraic geometry. Many talks will involve applications of representation theory to mathematical physics, combinatorics and algebraic geometry. The organizers expect the conference to be a major gathering of researchers in these fields and one of the most important mathematical events to take place in Moscow in the last few years. We expect that it will attract many graduate students and postdoctoral fellows, especially from the USA.In quantum physics, which describes the world of small objects (such as atoms, electrons, nuclei, etc) the state of a physical system is random and not definitively determined, unlike classical physics. In other words, states are no longer definite points of the classical space of states, but rather functions on the space of positions of the system, whose squared magnitude represents the chance the system will be found in that particular state. Such functions can be added and multiplied by numbers; that is, they form what is called a linear space. Symmetries of the system act by linear transformations of this space and therefore play an important role in studying quantum systems. The part of mathematics which studies actions of symmetries in linear spaces is called representation theory since we represent symmetries by linear transformations. Representation theory is thus extremely useful in quantum physics and other areas of physics, while physics, in turn, constantly provides deep insights into representation theory and other areas of mathematics. For example, in recent years the development of the representation theory of infinite-dimensional symmetries, coming from quantum field theory, has been an active area of research. During the conference leading mathematicians and mathematical physicists, many from the United States, will discuss the connections between representation theory and related fields in mathematics, as well as the connections to physics, especially in light of recent breakthroughs. The conference will be very useful for young mathematicians and graduate students who will attend the conference. The money from this award will support the travel and local expenses of US-based speakers and participants. Conference materials will be disseminated through the conference website http://bogomolov-lab.ru/rep2013/, which will allow the ideas presented at the conference to be accessed by a wide audience in the US and around the world. NSF support from this award will be advertised on the website, and US-based participants will be able to apply for this support.

“表示理论及其在组合学、几何和量子物理中的应用”会议将于 2013 年 12 月 13 日至 19 日在俄罗斯莫斯科独立大学举行。 这将是代表理论领域的顶尖数学家和年轻学者的一次重要聚会。 会议范围广泛，旨在介绍该领域一些最重要的最新进展和技术，特别是近年来出现的表示论、组合学、几何和物理学之间丰富的相互联系网络，这些网络极大地帮助了这些领域的发展。 会议讨论的主题包括代数群、几何表示论、顶点代数、无限维李代数、平面划分组合学、共形场论和枚举代数几何。 许多演讲将涉及表示论在数学物理、组合学和代数几何中的应用。 组织者预计这次会议将成为这些领域研究人员的一次重要聚会，也是过去几年在莫斯科举行的最重要的数学活动之一。 我们预计它将吸引许多研究生和博士后研究员，尤其是来自美国的研究生和博士后。 在描述小物体（如原子、电子、原子核等）世界的量子物理学中，与经典物理学不同，物理系统的状态是随机的且不确定。换句话说，状态不再是经典状态空间的确定点，而是系统位置空间上的函数，其平方大小代表系统处于该特定状态的机会。 此类函数可以进行数字的加法和乘法；也就是说，它们形成了所谓的线性空间。 系统的对称性通过该空间的线性变换起作用，因此在研究量子系统中发挥着重要作用。 研究线性空间中对称性行为的数学部分称为表示论，因为我们通过线性变换来表示对称性。 因此，表示论在量子物理学和其他物理学领域非常有用，而物理学反过来又不断地为表示论和其他数学领域提供深刻的见解。 例如，近年来，源自量子场论的无限维对称性表示论的发展一直是一个活跃的研究领域。 在会议期间，许多来自美国的顶尖数学家和数学物理学家将讨论表示论与数学相关领域之间的联系，以及与物理学的联系，特别是考虑到最近的突破。 这次会议对于参加会议的年轻数学家和研究生来说非常有用。 该奖项的资金将用于支持美国演讲者和参与者的旅行和当地费用。会议材料将通过会议网站http://bogomolov-lab.ru/rep2013/传播，这将使美国和世界各地的广大受众能够了解会议上提出的想法。 该奖项对 NSF 的支持将在网站上公布，美国的参与者将能够申请该支持。