Anglo-Franco-German in Representation Theory and its Applications

表示论是当今数学中最活跃的领域之一，在许多科学中都有应用，并与许多其他数学学科相互作用。这个美丽的主题起源于一个多世纪前德德金德写给弗罗贝尼乌斯的一封信。粗略地说，表示论可以被认为是对数学和物理中基本对称的研究，对称可以采取多种形式：群、结合代数、Hopf代数或李代数，仅举几例。表示理论的一个显著特点是它在数学和所有科学的其他主题上的相互作用和应用的丰富历史。例如，仅在过去的几年里，表征理论就与几何学、模型论、数论、概率论和理论物理学进行了卓有成效的互动。表征理论具有很大的多样性，可以用来统一不同的主题，目前是一项密集研究活动的核心(通过朗兰兹方案等世界范围的研究方案)。在这样的背景下，有必要为表征理论的研究者提供拓展更广阔视野的机会，并让其他研究者了解表征理论的最新发展。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/跨学科活动，促进表征理论与其他领域之间的互动。

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.