# Generalized traces and modified dimensions

SPEAKER: Nathan Geer

TITLE: Generalized traces and modified dimensions

ABSTRACT In this talk I will discuss how to construct generalized traces and modified dimensions in certain categories of modules. As I will explain there are several examples in representation theory where the usual traces and dimensions are zero, but these generalized traces and modified dimensions are non-zero. Such examples include the representation theory of the Lie algebra sl(2) over a field of positive characteristic and of Lie superalgebras over the complex numbers. In these examples the modified dimensions can be interpreted categorically and are closely related to some basic notions involving the representation theory. This joint work with Jon Kujawa and Bertrand Patureau.