Rate My Professor Brian Harbourne

Brian Harbourne is the Willa Cather Professor of Mathematics and a 2022 Fellow of the American Mathematical Society in the Department of Mathematics at the University of Nebraska-Lincoln. He earned his Ph.D. in 1982 from the Massachusetts Institute of Technology, completing his dissertation "Moduli of Rational Surfaces" under the advisement of Michael Artin. Harbourne has served on the faculty at the University of Nebraska-Lincoln for over three decades, receiving the College Distinguished Teaching Award in 1992. In 2020, he was appointed to the prestigious Willa Cather Professorship in recognition of his major contributions to algebraic geometry. His research has earned international acclaim, culminating in his election as an AMS Fellow and the organization of a dedicated conference, "Conference on Unexpected and Asymptotic Properties," in his honor at UNL in August 2023. He has also collaborated on NSF-funded projects to support graduate students and postdocs.

Professor Harbourne specializes in commutative algebra and algebraic geometry. Early work focused on the geometry of rational surfaces, complete linear systems, and anticanonical rational surfaces. His contributions extend to Hilbert functions of points in the plane, symbolic powers versus ordinary powers of ideals, star configurations in projective space, and asymptotic resurgences for ideals of points. Recent investigations address geproci point sets, unexpected hypersurfaces, the Containment Problem, line arrangements in the plane, and the Bounded Negativity Problem, including resolutions for fat point subschemes of the projective plane. Key publications include "Comparing powers and symbolic powers of ideals" with C. Bocci (arXiv 2007), "The geometry of rational surfaces and Hilbert functions of points in the plane" (1986), "Are symbolic powers highly evolved?" with C. Huneke (arXiv 2011), "Star configurations in P^n" with A.V. Geramita and J. Migliore (Journal of Algebra 2013), "Anticanonical rational surfaces" (Transactions of the American Mathematical Society 1997), "Negative curves on algebraic surfaces" (2013), "Asymptotic resurgences for ideals of positive dimensional subschemes of projective space" with E. Guardo and A. Van Tuyl (Advances in Mathematics 2013), and "The resurgence of ideals of points and the containment problem" with C. Bocci (Proceedings of the American Mathematical Society 2010). Harbourne has advised nine Ph.D. students, delivered over 20 invited lectures at international venues such as Oberwolfach, CIRM Luminy, and various university seminars, and maintains an active presence in the field through arXiv preprints.