Ottawa Student Seminar

Women have been historically barred from academia but have nonetheless continually made remarkable contributions all the while facing some of the harshest of circumstances. We will overview women’s role in the invention of mathematics, some particularly noteworthy mathematicians as well as some of the ways brilliant but forgotten women have contributed to mathematics indirectly.

We give a brief introduction to predator-prey dynamics and discuss how to model such systems. We then consider a scenario where two predators share a common prey, and one predator exhibits a seasonally-dependent switch in predation pattern. The goal is to construct a suitable model for this system, study the dynamics of this model and observe how varying season lengths in a year affects the coexistence of the three species.

We give a brief overview of the basics of category theory. Specifically, we will discuss monoidal categories and the simplifications that can be made using string diagrams.

First rigorously defined by J. Peter May in 1972, operads are a lesser-known algebraic structure centred around the concept of "multicomposing" several elements together at the same time. We give an overview of the basic definitions and fundamental examples for operads, with a focus on visualization via tree diagrams.

We give the definition of a strict monoidal category and show how we can describe the morphism space of these categories using pictures involving oriented lines, called string diagrams. Using these diagrams, we define a category, H’, and describe its relationship with the Heisenberg algebra. Many examples will be given throughout.