Perspectives in Representation Theory

表示论的观点

• 批准号: 1205125
• 负责人: Gregg Zuckerman
• 金额: $ 4.99万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-02-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1205125&HistoricalAwards=false
• 关键词: Perspectives; Representation; Theory

The conference "Perspectives in representation theory" will be a meeting of mathematicians working in representation theory, with an emphasis on its relations to other subjects (notably, topology, algebraic geometry, number theory, and mathematical physics). The conference will be held on May 12-17, 2012 at Yale University, in honor of the 60th birthday of Prof. Igor Frenkel. The speakers have made and continue to make major contributions to the field, and are responsible for a vast web of connections of representation theory with other areas of mathematics and physics. The aim of the conference is to present current progress on the following (interrelated) topics: vertex operator algebras and chiral algebras, conformal field theory, the (geometric) Langlands program, affine Lie algebras, Kac-Moody algebras, quantum groups, crystal bases and canonical bases, quantum cohomology and K-theory, geometric representation theory, categorification, higher-dimensional Kac-Moody theory, integrable systems, quiver varieties, representations of real and p-adic groups, and quantum gauge theories. Thus the conference will be an occasion to discuss representation theory in the context of its connections with numerous other subjects, and to discuss some of the most recent advances in representation theory, including those which occurred thanks to application of techniques in other areas of mathematics and physics, including ideas from quantum field theory and string theory. Further details can be found on the conference website at http://www.math.yale.edu/frenkel60Algebra is one of the oldest areas in mathematics. It encompasses a wide range of subjects from simple algebraic equations and polynomials to linear and abstract algebra. The study of symmetries is related to a branch of algebra called 'representation theory'. Representation theory has a vast array of applications in other areas of mathematics and physics. It is often through the study of representations that we learn about the innermost workings of our physical universe. While the origins of representation theory are algebraic, modern representation theory incorporates ideas from other branches of mathematics such as geometry, combinatorics, and category theory (a theory whose aim is to organize mathematical structure). These connections to new fields have both increased our knowledge in the area of representation theory as well as developed new applications of its ideas. The conference "Perspectives in representation theory" will be a gathering of some of the world's leading experts in this exciting field.

“表示理论的视角”会议将是研究表示理论的数学家的会议，重点是它与其他学科（特别是拓扑、代数几何、数论和数学物理）的关系。会议将于2012年5月12日至17日在耶鲁大学举行，以纪念伊戈尔·弗兰克尔教授60岁生日。演讲者已经并将继续为该领域做出重大贡献，并负责将表征理论与其他数学和物理领域联系起来的庞大网络。会议的目的是介绍下列（相互关联的）主题的最新进展：顶点算子代数和手性代数、共形场论、（几何）朗兰兹规划、仿射李代数、Kac-Moody代数、量子群、晶体基和正则基、量子上同调和k -理论、几何表示论、分类、高维Kac-Moody理论、可积系统、颤变、实数群和p进群的表示、量子规范理论。因此，这次会议将是一个讨论表征理论与许多其他学科联系的场合，并讨论表征理论的一些最新进展，包括那些由于在其他数学和物理领域的技术应用而发生的进展，包括量子场论和弦理论的思想。更多的细节可以在会议网站http://www.math.yale.edu/frenkel60Algebra上找到，这是数学中最古老的领域之一。它涵盖了从简单的代数方程和多项式到线性和抽象代数的广泛主题。对称的研究与代数的一个分支“表示理论”有关。表征理论在数学和物理的其他领域有广泛的应用。通常是通过对表征的研究，我们了解到物质世界最深处的运作。虽然表示理论的起源是代数的，但现代表示理论融合了其他数学分支的思想，如几何、组合学和范畴论（旨在组织数学结构的理论）。这些与新领域的联系既增加了我们在表征理论领域的知识，也开发了表征理论思想的新应用。“表征理论的视角”会议将是这个令人兴奋的领域的一些世界领先专家的聚会。