Research is formalized curiosity. It is poking and prying with a purpose. It is a seeking that he who wishes may know the cosmic secrets of the world and they that dwell therein.
Zora Neale Hurston
My PhD is in the area of mathematics called model theory. I give a more mathematical description of the field in the Model theory section. To get a rough idea, think of a “model” as a really large relational database, with attributes and functions and a way to select sets of records based on queries (expressions in a formal language that use the functions and attributes of the database). Model theory studies properties of classes of models, properties of the subsets of models that can be “selected”, and connections between these properties. One of the more recent strands in my research explores the connections between model theory and machine learning.
Studying very abstract mathematical objects often helps better understand specific applied problems. One such example involves applications of algebraic geometry (fairly abstract mathematics) to approximation theory (area of mathematics used, for example, in computer-aided design applications). I describe this more on the Approximation theory page.
Pretty much every university in the US has mathematics placement: a formal decision process to determine the level of mathematics courses for which a newly admitted student is ready. My colleagues and I explore how well the placement process works (and how can we tell whether or not it is working). The details are on the Math placement effectiveness page.