Human
I am a professor of mathematics at the University of Florida. I work in combinatorics, with a focus on structure and growth in discrete systems. Some of that work involves computation; some involves AI.
I tend to think of mathematics as the study of patterns that are simple to describe but resistant to complete understanding. Much of my work focuses on permutations and the ways local constraints force global behavior. When I am not thinking about those, I am usually building something, teaching something, or writing something down so someone else can use it.
Mathematics
I study structure in discrete objects. Among the simplest such objects are permutations. They are often introduced as ways of arranging distinct elements, but I prefer to view them as points in the plane: one point in each row and column, forming a geometric pattern. This perspective makes structural questions more visible.
A central theme of my research is the growth of permutation classes. Given a class defined by forbidden patterns, how quickly can it grow? Which real numbers arise as growth rates? Below certain thresholds the possibilities are rigid and classifiable; beyond them, the landscape becomes dense and intricate.
I have written a survey on permutation classes (arXiv, published) and coauthored the seventh edition of Graphs & Digraphs. Publication lists are available on Google Scholar, arXiv, and zbMATH. Slides for a few of my talks are available online. My CV is here.
Constructions
Whenever possible, I like to build things. Ideally, they are useful. Failing that, they are at least enjoyable.
HaLLMos is an AI tool that gives students feedback on their proof attempts. Students submit proofs, receive feedback, and revise, getting more practice than any instructor could respond to. It is freely available to use by students and instructors. Co-PIs on the project are Sarah Sword, Jay Pantone, and Ryota Matsuura.
Digit Party, co-created with Robert Brignall, is a small puzzle game inspired by "Neighbors" from Math Games with Bad Drawings.
I made Ad Free Clock because I couldn't find one to use when giving exams. It is exactly what it sounds like.
Teaching
Lately I've been teaching introduction to proofs, real analysis, combinatorics, and graph theory at the undergraduate level, and combinatorics at the graduate level. More details are on my UF homepage.
Contact
X · Bluesky · Mathstodon · MathOverflow