PIMS/UNAM Algebra Summer School (06ss100)

Objectives

Recent developments consider geometric objects associated to module categories, such as varieties of algebras and modules, semi-stable representations and their moduli spaces. These topics require the use of tools of Algebraic Geometry, which relates with many branches of mathematics, such as, differential geometry, topology, number theory, analysis and differential equations. It is worth mentioning that the modern approach to the problem of classifying varieties involves classifying all possible embeddings into projective spaces. Homological methods in representation theory have also had important successes, where methods from the cohomology of finite groups are applied to understanding basic properties of modular representations, as well as for obtaining explicit calculations. In particular there has been recent progress in classifying endo-trivial modules using these methods. Representation theory has proved equally important in the realm of infinite dimensional algebras, where it has long been utilized to linearize the study of objects such as infinite groups or differential operators. It has led, in particular, to the study of algebras with multiplicative twists, which have played key role the development of quantum groups. The algebraic side of this field includes the study of the noncommutative version of classical algebraic geometry.

The PIMS/UNAM Algebra Symposium has the goal of bringing together researchers from Canada, Mexico and the United States involved in areas of algebra which touch upon the themes outlined above. This will lead to important interactions between PIMS researchers already involved in a Collaborative Research Group (CRG), as well as helping establish a significant connection to the highly regarded algebra community in Mexico.