# Logic seminar: Lorna Gregory (University of East Anglia)

Dates: | 14 February 2024 |
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Times: | 15:15 - 16:15 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |

Title: Pseudofinite-dimensional Modules over Finite-dimensional Algebras

Abstract:

The representation type of a finite-dimensional k-algebra is an algebraic measure of how hard it is to classify its finite-dimensional indecomposable modules.

Intuitively, a finite-dimensional k-algebra is of tame representation type if we can classify its finite-dimensional modules and wild representation type if its module category contains a copy of the category of finite-dimensional modules of all other finite-dimensional k-algebras. An archetypical (although not finite-dimensional) tame algebra is kx. The structure theorem for finitely generated modules over a PID describes its finite-dimensional modules. Drozdâ€™s famous dichotomy theorem states that all finite-dimensional algebras are either wild or tame.

A long-standing conjecture of Mike Prest claims that a finite-dimensional algebra has decidable theory of modules if and only if it is of tame representation type. Most representation theorist are principally interested in finite-dimensional modules. A module over a k-algebra is pseudofinite-dimensional if it is a model of the common theory of all finite-dimensional modules. In this talk we will present work in progress around and in support of the following variant of Prest's conjecture: A finite-dimensional algebra has decidable theory of pseudofinite-dimensional modules if and only if it is tame.