International Conference on Representation Theory and Commutative Algebra

表示理论与交换代数国际会议将于4月24日至27日在康涅狄格大学举行，将把各个层次的研究人员聚集在一起，进一步探索标题中提到的领域之间的联系。广义地说，表征理论试图用具体的术语来实现抽象的代数对象，通常是通过矩阵集合或其他易于理解的结构。其理念是，为了更好地探索一个群体（作为物体的对称性产生）或一个代数（作为物体之间的函数产生）或任何其他相关的代数结构的行为，人们可以从描述这种结构可以作用于集合的所有方式开始。写下这样的特征可能是一个非常困难的问题，但有一些数学领域可以让我们更深入地理解这些行为，包括交换代数。本次会议将从这一观点来研究表征理论所能收集到的数据。会议将设法传播最近的成果，同时邀请下一代初级研究人员参与新的发展。专家们将分享理论进展并为问题提供视角，早期职业参与者将通过海报展示讨论他们的贡献。欲了解更多详情，请参阅http://condor.depaul.edu/acarro15/ICRTCA.html代数几何技术已应用于问题的表示理论自70年代初。几何观点被Kac用于确定颤振的不可分解表示，被Jerzy Weyman用于构造定义模变理想的自由分辨，被Jerzy Weyman和Harm Derksen用于证明Littlewood-Richardson系数的饱和性质，被Alastair King用于构造表示的模空间。这次会议的目的是解决从这些几何方法演变而来的几个具体问题和一些问题。

The International Conference on Representation Theory and Commutative Algebra, to be held April 24-27 at the University of Connecticut, will bring researchers of all levels together to further explore the connections between the fields mentioned in the title. Broadly speaking, representation theory attempts to realize abstract algebraic objects in concrete terms, usually via collections of matrices or other well-understood constructs. The philosophy is that to better explore the behavior of a group (arising as symmetries of objects) or an algebra (arising as functions between objects) or any other pertinent algebraic structure, one can start by characterizing all manners in which such a structure can act upon a set. Writing down such a characterization can be a tremendously difficult problem, but there are fields of mathematics that can lead to deeper understanding of these actions, including commutative algebra. This conference will examine the data that can be gleaned about representation theory from this point of view. The conference will seek to disseminate recent results while inviting the next generation of junior researchers to take part in new developments. Experts will share theoretical progress and lend perspective to the questions, and early career participants will discuss their contributions through poster presentations. For more details see http://condor.depaul.edu/acarro15/ICRTCA.html Algebro-geometric techniques have been applied to problems in representation theory since the early seventies. The geometric point of view was put to use by Kac in locating indecomposable representations of quivers, by Jerzy Weyman in constructing free resolutions of defining ideals of module varieties, by Jerzy Weyman and Harm Derksen in proving the saturation property for Littlewood-Richardson coefficients, and by Alastair King in constructing moduli spaces of representations. The aim of this conference is to address several specific questions and a number of problems that have evolved from these geometric approaches.