booklet - CUMC - Canadian Mathematical Society

librium points, and determine what biological factors have a destabilizing effect onthese systems. The topics I cover include single-species density dependence models,discrete-time models and the effects of time delays. I continue the discussion withinteracting populations, specifically density dependent predator-prey models followedby discrete-time predator-prey models. I finish on the topic of spatially structured models,how to formulate them, and provide examples of linear and nonlinear problems. Iused the magical wonders of MATLAB to provide visual examples for a variety of themodels throughout this discussion.Required Background: A course in Ordinary Differential Equations.LIE ALGEBRAS AND THEIR REPRESENTATIONSKATHLYN DYKESLie Algebras are an important algebraic structure used in studying many differentthings from differential Galois theory to quantum mechanics and particle physics. Thistalk will provide an introductory first look at Lie Algebras and then move onto discusstheir more abstract and theoretic properties. This will include a look at the structure ofrepresentations of lie algebras that is currently being worked on by a handful of expertsin the field.Required Background: Basic AlgebraSEQUENCES OF SUBSETS OF EUCLIDEAN SPACE AND THEIR LIMITS: A CAUTION-ARY TAILKERRY MANUEL CERQUEIRAAfter learning some introductory analysis concepts we realize how to generalizethe concept of a limit, and subsequently how to take limits of all sorts of mathematicalobjects. After being confused by the Weierstrauss function, maybe we realize that thisprocess is a good way to generate pathological objects. In this talk we will explorewhat it means to take a sequence of subsets of Euclidean space (ignoring for a momentthat this is a fairly obvious sort of idea and that consequently there is probably a goodreason it’s not often talked about) with the aim of coming up with a definition andproving some elementary theorems that come about as a consequence. After that, we’lltry to define a metric on the power set of Euclidean space in n dimensions. A discussionof why this is problematic, and about how the wrong question can often be just asinformative as the right answer, will follow.Required Background: Some calculus, analysisTHE METRIC SPACE INDUCED BY THE RIEMANNIAN MANIFOLDKEVIN MATHERThe aim of this talk will be to give an introduction on how to construct a metricspace if we are given an Riemannian manifold. In order to do this, we will first giverise to a concept of lengths of tangent vectors. From this we can give an idea of thelength of a curve as the integral of the length of its velocity vector field. This will allow34