Fall 2022

Kolton O'Neal

Mentor: Ryan Watson

Title: The Long Exact Sequence in Homology

Description: Homological algebra studies R-modules, which can be thought of as a generalization of groups, rings, and vector spaces, by examining sequences of them with certain properties. These sequences are called chain complexes. In this talk, I will explain (or at least, state) an important result in homological algebra called the long exact sequence in homology.

Dakota Andrews

Mentor: Abbey D'Ovidio

Title: Rest Points and Stability of Competitive Populations

Description: Just as a single differential equation can have equilibria, a system of differential equations has what is referred to as rest points. These rest points can either be stable or unstable and behave differently based on the eigenvalues of the linearized system. In this presentation we will walk through the methods of analyzing the rest points of a system, and then look at a specific system modelling two competitive populations. This competitive model can be applied to populations like healthy vs. cancer cells, a plant vs. an invasive species, and many other models.

Justin Ho

Mentor: Nikola Kuzmanovski

Title: Introduction to Ramsey Theory

Description: This talk will provide an introduction to Ramsey Theory, including some interesting ideas that come from it and what kinds of questions it tries to solve.