Computing characters and representations of finite groups of Lie type in their defining characteristic

The representations in question are parameterized in terms of \emph{highest weights} and are closely related to rational representations of reductive algebraic groups and their Lie algebras. The degrees of the representations are generally not known (but in some cases there exists a conjecture by Lusztig). An overview on this background will be given, as well as some results and applications.

In this talk \emph{computing} means a practical computing of explicit characters and representing matrices using a computer.