International Conference on Representation Theory and Commutative Algebra

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.