Lorna Gregory
(University of Manchester)
Interpretation Functors, Wild Algebras and Undecidability

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 finite-dimensional k-algebra is of wild representation type, a notion coming from representation theory, then it has undecidable theory of modules.

A finite-dimensional k-algebra is said to be of wild representation type essentially if the problem of classifying its indecomposable finite-dimensional 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.