Lorna Gregory

In this talk I will present results about the undecidability of theories of modules over certain rings. In particular, I will focus on attempts to prove a conjecture of Prest which says that if a finitedimensional kalgebra is of wild representation type, a notion coming from representation theory, then it has undecidable theory of modules. A finitedimensional kalgebra is said to be of wild representation type essentially if the problem of classifying its indecomposable finitedimensional modules is impossible, in a sense to be made precise during the talk. A key tool in this work is the notion of interpretation functors between categories of modules. I will explain how these functors give rise to interpretations in the model theoretic sense and give some examples. All necessary background material will be introduced. 