Foundations (logic and set theory)

Description


Faculty members involved

Thomas Kucera (link) works in mathematical logic (model theory) and applications of model theory to module theory and ring theory. His particular interest is in the structure of injective modules and related objects, such as pure-injectives, and their connections to parts of ring theory, especially non-commutative localization.

The key concept is that of a pure-injective module, which has natural, well-motivated definitions both as an object of interest in mathematical logic and as an object of interest in algebra. Injective modules over (even one-sided) noetherian rings are natural examples of a special kind of pure-injective module, called "totally transcendental". It is hoped that model-theoretic techniques for studying structural questions will lead to interesting and useful purely algebraic results.

Current students and postdoctoral fellows

  • Julian Salamanca Tellez (Ph.D., Supervisor: Kucera/Sichler)

Representative recent publications

  • C. Enns and T. G. Kucera. Purity and pure-injectivity for topological modules. Models, Logics and Higher Dimensional Categories: a Tribute to the Work of Mihály Makkai, pp55-77, 2011.
  • T. G. Kucera. The structure of indecomposable Ʃ-pure-injective modules (a survey of basic results and problems). Proceedings of the International Conference on Modules and Representation Theory, pp85--102, 2009.
  • T. G. Kucera. Explicit descriptions of the indecomposable injective modules over Jategaonkar's rings. Communications in Algebra, vol. 30, 2002.
  • T. G. Kucera and Ph. Rothmaler. Pure-projective modules and positive constructibility, Journal of Symbolic Logic, vol. 65(1), 2000.

News

MathCamp 2017 information is online.

Manitoba Workshop on Mathematical Imaging Science Friday, May 5, all day, Robert Schultz Lecture Theatre, details.

In an effort to help students, the Math department has put together the LevelUp program. See details here. Video explaining registration process is here.

Events

Thursday, May 4th, 2017 at 15:30, 418 Machray Hall
Tommy Kucera
Fibonacci and The Liber Abaci
(Seminar series : Colloquium)

Friday, May 12th, 2017 at 15:30, 418 Machray Hall
John Dallon
Modeling Amoeboidal Cell Motion -- Force vs Speed
(Seminar series : Colloquium)

Friday, August 4th, 2017 at 15:30, 418 Machray Hall
Jose Aguayo
TBA
(Seminar series : Colloquium)