Ph.D. (mathematics), University of Missouri (2015)
M.A. (mathematics), University of Missouri (2011)
B.A. (mathematics and physics), William Jewell College (2008)
My research lies at the junction of Harmonic Analysis and Partial Differential Equations (PDEs), and a large portion of my work falls under the scope of the general program aimed at studying the interrelationship between geometry and analysis by addressing issues such as how to relate the geometry of an environment to the analysis it can support. This focus has recently led me to work on problems in an area of mathematics called Analysis on Metric Spaces which center around extending results obtained in the “flat-space” Euclidean setting to more general nonsmooth environments that lack the resourceful nature of the Euclidean structure. This field emerged in the 1990s and has continued to maintain its significance, evolving into a beautiful multifaceted theory with far-reaching implications in many branches of mathematics. In particular, over the last few years, I have been studying properties of Hardy and Sobolev spaces and their applications to certain classes of PDEs.
I love to teach a wide variety of courses offered in the mathematics curriculum, ranging from first-year calculus to upper-level proof-based courses. Doing so affords me the opportunity to work with students who are at different stages in their education and who have different academic interests. I truly enjoy the time I spend with students, and I aim to incorporate interactive components into each class that I teach. I am also interested in pedagogy as well as questions arising in math education.
Please see my website for a list of my publications, CV, teaching materials, etc.