Nathan M. Dunfield

Nathan M. Dunfield is a Professor of Mathematics at the University of Illinois at Urbana-Champaign (UIUC), affiliated with the College of Liberal Arts & Sciences. He holds a PhD from the University of Chicago and has held positions at Harvard University and the California Institute of Technology before joining UIUC in 2007. His research focuses on 3-dimensional geometry and topology, hyperbolic geometry, and their connections to number theory and geometric group theory. Dunfield is a Fellow of the American Mathematical Society (since 2013) and collaborates with researchers in physics, computer science, and algebraic geometry.

Education History: PhD from the University of Chicago (20th century), prior roles at Harvard and Caltech. Current research interests include experimental mathematics, topological invariants, and applications of geometric techniques to problems in algebra and number theory. He develops computational tools like the SnapPy software for studying 3-manifolds.

Key contributions include work on essential surfaces in 3-manifolds, random 3-braids, and algorithmic topology. Dunfield advises current PhD students Brevan Ellefsen, Lara Lahey, and Shana Li, and has mentored numerous graduated students. His work integrates theoretical insights with computational methods, exemplified by collaborations on projects like the Virtual Haken Conjecture and spatial graph enumeration in engineering systems.

He maintains active research through grants and collaborations, including contributions to open-source software and participation in interdisciplinary initiatives. Dunfield’s labs and teams involve computational topology projects, such as the SnapPy development and CompuTop collaborations, advancing both theoretical understanding and practical tools in low-dimensional topology.