Research Interests: 

I’m interested principally in Spectral Theory, a branch of Functional Analysis, which itself combines Calculus and Linear Algebra. 

With fewer buzzwords: in various physics-inspired settings, mathematical modeling tools called linear operators often have a collection of associated characteristic values, also known as eigenvalues, that collectively describe much of the structure of the linear operator. We often start with a simple operator for which the exact eigenvalues are known, and slowly adjust the operator to become more physically realistic -- which alters the set of eigenvalues as well. What can be said about the eigenvalues after these changes to the operator? Are they all positive, or can some of them be negative? Are they all real numbers, or do some of them leave the real-number line and enter the rest of the complex-number plane? (And if so, can they ever return?) These are the questions I study.

Teaching Interests:

I like teaching Calculus II, especially infinite-sequences-and-series, with the necessary logic and helpful experimentation to appreciate them. 

Courses Taught: 

In my previous experience, I have taught, or assisted in teaching, every level of calculus, plus small amounts of linear algebra and differential equations.

This fall, I am teaching MATH 114: Mathematical Explorations and Math 119: Calculus I.