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.
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.
We will start with an introduction to the mod 2 Steenrod algebra,
and some structure theory for modules over its subalgebras due to Adams and
Margolis. In particular, there is a set of homology functors which detect
stable isomorphism, and there are subcategories of modules that are `local'
with respect to them.
Next, we specialize to the subalgebras relevant to real and complex K-theory,
called E(1) and A(1), where we can give quite precise descriptions of the
local modules. The Picard groups of these subcategories are sufficient to
detect the Picard group of the whole category and contain modules of geometric
General results obtained along the way allow us to begin to attack the
analogous questions for E(2) and A(2)-modules.
Applications include better descriptions of polynomial algebras as modules
over the Steenrod algebra, and of the values of certain generalized cohomology
theories on the classifying spaces of elementary abelian groups.
Homological algebra of vector spaces is well understood. In functional analysis, many infinite dimensional vector spaces also contain analysis information. A diffeological vector space is a vector space with a compatible (generalized) smooth structure. In this talk, I will present a non-trivial example from functional analysis under the framework of diffeological vector spaces, see how the generalized smooth structure can be used to generalize a known result from analysis, as a motivation for the development of homological algebra of diffeological vector spaces. Then I will talk about the similarity and difference between this homological algebra and the homological algebra of R-modules. If time permits, some open questions will be discussed at the end.
Our old website has not been maintained for more than two years, and is no longer accessible from this page. If you require access to it, please email Stuart Rankin.