I received my Ph.D. in mathematics from the University of Victoria. My research area is in a branch of mathematics known as functional analysis, which may be thought of as a combination of linear algebra, calculus, and geometry. Specifically, I focus on dynamical systems, or, how systems change over time, and how techniques from functional analysis can help us understand the structure of these systems. Studying dynamics is important because the world around us changes constantly in all sorts of ways, and by understanding how systems change over time, we can use them to model real-world situations to make accurate predictions about how these situations might evolve.

Given a dynamical system, we can encode the dynamics using objects from linear algebra (matrices or linear operators), and by doing this, tools from functional analysis such as spectral theory allow us to gain insights into the patterns and symmetries that emerge, and therefore answer questions about the underlying system.

The beautiful thing about working at the intersection of two areas is that it provides a setting to find connections between ideas that were previously thought to be unrelated. Indeed, this is the essence of mathematics: finding creative ways to solve fundamental but challenging problems so that we may better understand the diverse phenomena around us.

My dissertation can be found here.