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.
In various mathematical contexts it is possible to find a single object which, when subjected to a countable process, yields approximations to the whole universe under study. Such an object is termed "universal" and, contrary to expectations, such objects often turn out to be generic rather than exceptional. This talk will focus on this phenomenon in respect of the Taylor series of a holomorphic function, and how the partial sums behave outside the domain of the function. It will discuss how potential theory reveals much about the boundary behaviour of such functions, and their relationship with conformal mappings.
Ordered commutative monoids are mathematical structures that
are simple to define, yet display a very diverse phenomenology. I will
introduce these structures and explain how they formalize situations
in which one deals with resource objects and how they can be combined
with each other or converted into each other, such as the molecules in
a chemical reaction like $2H_2 + O_2 \rightarrow 2H_2O$. Some standard theorems
of functional analysis yield results on ordered commutative monoids,
which in turn have applications to Shannon's theory of communication
and the ordered commutative monoid of graphs.