Generalized traces and modified dimensionsIn this talk I will discuss how to construct generalized traces

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 trace

and dimension 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.