Rate My Professor Brian Harbourne

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.