Association for Symbolic Logic Tutorial

Association for Symbolic Logic Tutorial: From noncommutative algebra to model theory - via Poisson algebras, Parts I & II, organized by Reed Solomon, ASL; Wednesday, 9:00–10:00 am and 2:00–3:00 pm. The speaker for these tutorial sessions is Omar Leon Sanchez, University of Manchester. In these tutorials he will describe some recent (8 years, or so, ago) interactions between representations of algebras (noncommutative algebra) and model theory (mathematical logic). The Dixmier-Moeglin programme, on the algebraic side, attempts to understand irreducible representations in topological and algebraic terms. For interesting classes of graded algebras, significant information can be obtained from studying the associated Poisson algebras, and this is where model theory comes into the picture. Using tools from the model theory of differentially closed fields, we have answered several questions posed by the algebraic community (some positively and some negatively). Furthermore, a model-theoretic abstraction of the Dixmier-Moeglin programme has been formulated. Omar Leon Sanchez will give an introduction to the subject, explain some recent results, and pose some still open problems.