Contact Information
378 Altgeld Hall, MC-382
1409 W. Green Street
Urbana, IL 61801
Biography
Since the summer of 2007, I have been an Associate Professor here at the University of Illinois at Urbana-Champaign. Previously, I spent four years at Harvard and four years at Caltech after getting my PhD from the University of Chicago sometime back in the 20th century. In 2013, I became a Fellow of the American Mathematical Society.
Research Interests
3-dimensional geometry and topology, hyperbolic geometry, geometric group theory, experimental mathematics, connections to number theory.
Research Description
My research area is the topology and geometry of 3-manifolds. I was attracted to it because of the richness it acquired from Thurston’s revolutionary work starting in the 1970s. His key insight was that many 3-manifolds admit homogeneous Riemannian metrics, and that one can study the topology of a 3-manifold via this geometry. This profusion of geometry has now been stunningly confirmed by Perelman’s proof of the Geometrization Conjecture. As a direct result, while my work has focused on what initially seem like purely topological problems, in fact I have used a broad range of techniques to attack them, including hyperbolic geometry, number theory, and algebraic geometry, as well as more obviously related areas such as combinatorial group theory and the theory of foliations. These connections to other fields have led me to collaborate with number theorists, theoretical physicists and computer scientists, and in my papers I've used both the Langlands Conjecture and the Classification of Finite Simple Groups, as well as such topological oddities as “random 3-manifolds”.
External Links
Recent Publications
Dunfield, N. M., Obeidin, M., & Rudd, C. G. (2022). Computing a Link Diagram from Its Exterior. In X. Goaoc, & M. Kerber (Eds.), 38th International Symposium on Computational Geometry, SoCG 2022 [37] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 224). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SoCG.2022.37
Dunfield, NM. M., Garoufalidis, S., & Rubinstein, J. H. (2022). Counting essential surfaces in 3-manifolds. Inventiones Mathematicae, 228(2), 717-775. https://doi.org/10.1007/s00222-021-01090-w
Peddada, S. R. T., Dunfield, N. M., Zeidner, L. E., James, K. A., & Allison, J. T. (2021). Systematic enumeration and identification of unique spatial topologies of 3D systems using spatial graph representations. In 47th Design Automation Conference (DAC) [V03AT03A042] (Proceedings of the ASME Design Engineering Technical Conference; Vol. 3A-2021). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC2021-66900
Agol, I., & Dunfield, N. M. (2020). Certifying the thurston norm via SL(2,C)-twisted homology. Annals of Mathematics Studies, 2020(205), 1-20.
Dunfield, N. M. (2020). A census of exceptional Dehn fillings. In Contemporary Mathematics (pp. 143-155). (Contemporary Mathematics; Vol. 760). American Mathematical Society. https://doi.org/10.1090/conm/760/15289