I view mathematics through the lens of natural philosophy, and that perspective guides my interests: how can we see why things are the way they are, and not just verify that they are? Could Aristotle, for instance, have proven that regular tetrahedra don’t fill space? (He believed they did, and the mistake went largely unchallenged for well over a thousand years.) My research has followed that thread through discrete geometry and geometric optimization: how tightly shapes like cylinders, pentagons, and spheres can pack, how evenly points can be spread over a sphere, and why some knotted rope cannot be pulled apart. I look for arguments, synthetic or analytic, that give that kind of Anschauung, and for where computer-assisted proof can extend it. To that end, I also build models of some of the objects I study. The same perspective draws me to the questions beneath the subject: what mathematical objects are, what logic can and can’t capture, and how mathematics and its practice, purpose, and language have shaped one another through history.
I came to Lawrence in 2023 after working as an FWF postdoctoral researcher at Graz University of Technology and holding positions at Vanderbilt University and the University of Georgia. I have also been a visiting scholar at ICERM, MSRI, the Erwin Schrödinger Institute, the Aspen Center for Physics, and the Fields Institute.
If you are a student interested in research, whether a directed study or a summer project, please email me and we can talk about possible problems. If you’d like to work as a tutor or teaching assistant, please get in touch as well.
