Bowdoin

Given a vector space V over a field K, let End(V) denote the algebra of linear endomorphisms of V. If V is finite-dimensional, then it is well-known that the diagonalizable subalgebras of End(V) are characterized by their internal algebraic structure: they are the subalgebras isomorphic to K^n for some natural number n. 

In case V is infinite dimensional, the diagonalizable subalgebras of End(V) cannot be characterized purely by their internal algebraic structure: one can find diagonalizable and non-diagonalizable subalgebras that are isomorphic.  I will explain how to characterize the diagonalizable subalgebras of End(V) as topological algebras, using a natural topology inherited from End(V).  I will also illustrate how this characterization relates to an infinite-dimensional Wedderburn-Artin theorem that characterizes "topologically semisimple" algebras.

One of the things sustainability applications have in common with industrial applications is their close connection with decision-making and policy. We will discuss how a decision-support viewpoint may inspire new mathematical questions. For example, the concept of resilience (of ecosystems, food systems, communities, economies, etc) is often described as the capacity of a system to withstand disturbance and retain its functional characteristics. This has several familiar mathematical interpretations, probing the interaction between transient dynamics and noise. How does a focus on resilience change the modeling, dynamical and policy questions we ask? I look forward to your ideas and discussion.