The winter school will be aimed at graduate students and postdoctoral fellows. It will feature two 12-hour mini-courses augmented by exercise sessions.
Introduction to categorification
Speaker: Alistair Savage (University of Ottawa)
This mini-course will serve to introduce students to the new and exciting field of categorification. Its goal is to prepare students for the workshop “Geometric representation theory and categorification”. In the first week, a recent approach to the representation theory of the symmetric group will be presented (as found, for instance, in the first few chapters of the book Linear and projective representations of symmetric groups by Kleshchev). This will provide students with a novel approach to the subject that is well suited to the ideas of categorification. In the second week, the basic ideas of categorification will be presented, with a special emphasis on explicit examples (drawing, in particular, from the material in the first week).NOTES AND REFERENCES
Introduction to Kac-Moody and related Lie algebras
Speaker: Erhard Neher (University of Ottawa)
While many universities offer a first course on Lie algebras, a second course on Lie algebras is usually not part of the graduate program. This mini-course will present the basic structure theory of Kac-Moody algebras with a special emphasis on affine Lie algebras (as found, for instance, in the first eight chapters of the book Infinite- dimensional Lie algebras by Kac). Some related non-Kac-Moody algebras, such as toroidal algebras, will also be presented. This course will prepare students for the mini-course “Representation theory of semisimple, affine and Kac-Moody algebras” in the second winter school (February 24 - March 7, 2014).NOTES AND REFERENCES