In collaboration with Usman Hafeez, I am currently an advisor for undergraduate research through the University of Kentucky Mathematics Lab. Our group primarily focuses on dynamical systems and mathematical ecology. 

I have previously co-advised undergraduate research with Dr. Kyle Hammer, who is currently a visiting assistant professor at the University of Cincinnati.

2026-2027 Project: Replicator Dynamics of Many-Strategy Populations

Click here to see the slides presented at the interest meeting on August 28th.

Here are some of the questions we will be thinking about in this project:

• The Theme: Replicator dynamics is completely understood with three or fewer strategies. What can one understand about it with four or more?

•  How do the symmetric and skew-symmetric parts of payoff matrices affect the dynamics?

•  Which strategies lead to chaotic dynamics with four or more strategies?

•  How do mechanisms other than natural selection (e.g. mutation, gene flow) affect the dynamics?

•  What if the fitness of each strategy depends on time? What if it doesn’t depend linearly on the state vector?

•  How do perturbations of the payoff matrix by small random matrices affect the dynamics?

• And other questions that you come up!

Pictures

Posters

Matrix Population Modeling Group (2025-2026): Coupled Matrix Population Models for Predator-Prey Interaction (pdf)