The Mathematical and Computational Sciences at Western are represented by four separate departments: Applied Mathematics, Computer Science, Mathematics, and Statistical & Actuarial Sciences. The Department of Mathematics has established research groups in several areas of contemporary mathematics including algebra, analysis and analytic geometry, homotopy theory, and noncommutative geometry.

Upcoming Events

Each week the Department of Mathematics hosts a wide variety of seminars and events. For a comprehensive list of events, please consult our departmental calendar.

A major open problem in current Galois theory is to characterize those profinite groups which appear as absolute Galois groups of various fields. Obtaining detailed knowledge of the structure of quotients and subgroup filtrations of Galois groups of $p$-extensions is an important step toward a solution. We illustrate several techniques for counting Galois $p$-extensions of various fields, including pythagorean fields and local fields. An expression for the number of extensions of a formally real pythagorean field having Galois group the dihedral group of order 8 is developed. We derive a formula for computing the $\mathbb{F}_p$-dimension of an $n$-th graded piece of the Zassenhaus filtration for various finitely generated pro-$p$ groups, including free pro-$p$ groups, Demushkin groups and their free pro-$p$ products. Several examples are provided to illustrate the importance of these dimensions in characterizing pro-$p$ Galois groups. We also show that knowledge of small quotients of pro-$p$ Galois groups can provide information regarding the form of relations among the group generators.

More than 50 years ago, Laszlo Fuchs asked which abelian groups can be the group of units of a commutative ring. Though progress has been made, the question remains open. We answer this question in the case of indecomposable abelian groups by classifying the indecomposable abelian groups that are realizable as the group of units of a ring of any given characteristic. This is joint work (arXiv:1505.03508) with Keir Lockridge

This two-days workshop will consist of research talks by experts on three aspects of the subject:
I) Spectral invariants of noncommutative spaces and the spectral action principle,
II) Applications to the standard model of particle physics,
III) Cyclic cohomology and Hopf algebras.
For more information visit:
http://www-home.math.uwo.ca/~masoud/NCGUWO-2015/index.html

This two-days workshop will consist of research talks by experts on three aspects of the subject:
I) Spectral invariants of noncommutative spaces and the spectral action principle,
II) Applications to the standard model of particle physics,
III) Cyclic cohomology and Hopf algebras.
For more information visit:
http://www-home.math.uwo.ca/~masoud/NCGUWO-2015/index.html