Seminars take place on Monday afternoons 14:00 - 15:00. Everyone is welcome.
- October 10, (SCI 3.05), Chris Le Sueur (UEA), Infinite Games: Infintie Fun!
- October 17, (SCI 3.05), James East (University of Western Sydney), Idempotents in Planar Diagram Monoids.
- October 24, (SCI 0.31), Dr Lorna Gregory (Manchester), Title to be advised.
- November 7, (C.HALL 01.19) Speaker and Title To be advised.
- November 14, (ARTS 2.02), Speaker and Title To be advised.
- November 21, (SCI 3.05), Speaker and Title To be advised.
- November 28, (LT4), Speaker and Title To be advised.
- December 5, (LT4), Speaker and Title To be advised.
- December 12, (LT4), (Provisional) Professor Shahn Majid (QMUL), Title to be advised.
- December 19, (SCI 3.05), Speaker and Title To be advised
Chris Le Sueur: Infinite games arose out of the study of game theory in the 50s and grew into the field of Determinacy in Set Theory, where it is now one of the most important topics. I will give a "suitable for non-set-theorists" introduction to the area, culminating in a taste of the connections with large cardinals. I'll try to assume as little prior knowledge as possible, though if you can remember what ordinals and cardinals are, that will help!
James East: I will discuss recent joint projects with Igor Dolinka, Des FitzGerald, Robert Gray, James Mitchell, and others, on planar diagram monoids. These include families such as Temperley-Lieb monoids, Kauffman monoids and Motzkin monoids. Questions considered include: What are the idempotents of these monoids? How many idempotents are there? What is the idempotent-generated submonoid? What it the minimal number of idempotents required to generate these submonoids?
Lorna Gregory: In this talk I will give an overview of recent developments in the model theory of representations of finite-dimensional k-algebras.
These results will connect the representation type of a finite-dimensional algebra with the decidability of its theory of modules.
The theory of modules of a ring R is said to be decidable if there exists an algorithm which given a first order sentence in the language R-modules answers whether this sentence is true of all R-modules or not.
In order investigate the relationship between the representation type of a finite-dimensional algebra with the decidability of its theories of modules, we use interpretation functors which are an additive version of the model theoretic notion of interpretation. Algebraically, they are characterised as additive functors between module categories which commute with direct limits and products.
The representation type of a finite-dimensional k-algebra is a measure of how hard it is to classify its finite-dimensional indecomposable modules. Roughly, a finite-dimensional k-algebra is of wild representation type if classifying its finite-dimensional indecomposable modules is as hard as classifying those of the polynomial ring in two non-commuting variables. On the other hand, a finite-dimensional algebra is tame if for every dimension d, all but finitely many of the finite-dimensional indecomposable modules of dimension d are in finitely many 1-parameter families. According to Drozd, when k is algebraically closed, a finite-dimensional k-algebra is either tame or wild.
All terminology coming from model theory will be explained, as will the definitions of tame and wild representation type.