In this talk, I will give a high-level overview of the projects I worked on as an applied math Ph.D. candidate. Each project ties into my broader ambition of laying mathematical foundations for a data-driven approach to dynamics.

I will first discuss a policy for optimally timing observations of stochastic differential equations (SDEs). For context, imagine trying to infer the rate that insulin leaves a diabetic's bloodstream. Each insulin measurement requires a blood sample, so it should be taken judiciously.

Next, I will discuss the numerics that I use to simulate SDEs. This part of the talk will cover some of the deep connections between SDEs and ODEs.

Finally, I will summarize my research into the estimation of Floquet multipliers. (Floquet multipliers are to periodic steady states what Jacobian eigenvalues are to equilibria.) Here, the application is running: the mathematical questions I study provide insights into the way our neurosystem keeps us upright.