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Anglo-Franco-German in Representation Theory and its Applications

英法德的表征理论及其应用

基本信息

批准号：
EP/R009279/1
负责人：
Stephane Launois
金额：
$ 20.25万
依托单位：
University of Kent
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2018
资助国家：
英国
起止时间：
2018 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FR009279%2F1
关键词：
Anglo Franco German Representation Theory

项目摘要

Representation theory is one of the most active fields of mathematics today with applications in many of the sciences and interactions with many other mathematical disciplines. This beautiful subject originated in a letter to Frobenius by Dedekind more than a century ago. Roughly speaking, Representation Theory can be thought of as the study of basic symmetries in Mathematics and Physics, symmetries that can take many forms: groups, associative algebras, Hopf algebras or Lie algebras to name a few. A striking feature of Representation Theory is its rich history of interactions and applications to other topics in mathematics and to all sciences. For instance, in the last few years only, Representation Theory has fruitfully interacted with Geometry, Model Theory, Number Theory, Probability and Theoretical Physics to name a few. Representation Theory through its great diversity can be used to unify different themes and is currently at the heart of an intense research activity (through worldwide research programmes such as the Langlands programme). Given this background, it is necessary to provide researchers in Representation Theory with opportunities to develop a broader vision, and for other researchers to learn about the latest developments in Representation Theory. The proposed network will serve as a catalyser to stimulate interactions between Representation Theory and other areas, through the organisation of various interdisciplinary/intradisciplinary events in a coordinated effort with researchers from France and Germany.

表征理论是当今数学中最活跃的领域之一，应用于许多科学领域，并与许多其他数学学科相互作用。这个美丽的话题起源于一个多世纪前戴德金给弗罗本纽斯的一封信。粗略地说，表征理论可以被认为是对数学和物理中基本对称性的研究，这种对称性可以有多种形式：群、结合式代数、霍普夫代数或李代数等等。表征理论的一个显著特征是它在数学和所有科学的其他主题中相互作用和应用的丰富历史。例如，仅在过去几年中，表征理论与几何、模型论、数论、概率论和理论物理等学科进行了卓有成效的互动。表征理论通过其巨大的多样性可以用来统一不同的主题，目前是一个激烈的研究活动的核心（通过世界范围的研究项目，如朗兰兹项目）。在这种背景下，有必要为表征理论的研究人员提供发展更广阔视野的机会，并为其他研究人员提供了解表征理论最新发展的机会。拟议的网络将作为催化剂，通过与法国和德国的研究人员协调努力，组织各种跨学科/跨学科内的活动，刺激表征理论和其他领域之间的相互作用。