A pure mathematician, J.D. Quigley specializes in algebraic topology. He primarily focuses on the stable stems, which encode the possible relations between different high-dimensional spheres, and their applications to geometry, topology and algebra.
Quigley has published articles in a number of journals, including Geometry & Topology, Advances in Mathematics, and International Mathematics Research Notices. His research has been supported by grants from the National Science Foundation, the American Mathematical Society and the Simons Foundation. He is also co-Principal Investigator for an NSF Research Training Group grant supporting the development of an online research community centered around algebraic topology.
Before coming to the University of Virginia, Quigley earned his Ph.D. at the University of Notre Dame (2019). He has held postdoctoral positions at Cornell University, the Max Planck Institute for Mathematics in Germany, and the University of Oregon.
This year, Quigley is focused on understanding algebra-geometric analogues of the stable stems, as well as more classical geometric problems, like finding symmetries of “exotic spheres.” This fall, he will teach “Algebraic Topology II” and plans to co-organize the Topology Seminar and get involved with K-12 outreach.