James Dibble Ph.D.
- Ph.D. in Mathematics, Rutgers University-New Brunswick, 2014
- B.S. in Mathematics, University of Maryland, Baltimore County, 2006
- B.A. in English, University of Maryland, Baltimore County, 2006
James Dibble earned his Ph.D. in Mathematics from Rutgers University-New Brunswick in 2014, followed by visiting positions at Western Illinois University and the University of Iowa. He has also taught at the University of Pittsburgh and spent two semesters as a visiting scholar at Capital Normal University in Beijing. Originally from Maryland, he received bachelor's degrees in Mathematics and English from the University of Maryland, Baltimore County, where he graduated magna cum laude in 2006. He lives in Yarmouth with his wife, Sofia, and their three children.
My work is in differential and Riemannian geometry, area of mathematics in which one studies the geometry of curved surfaces and their higher-dimensional generalizations. Many of the problems that I have worked on are in the specific area of comparison geometry, in which one studies the relationship between the curvature of a space and its global shape or topology. I am particularly interested in questions about geodesics, especially closed geodesics, and spaces with no conjugate points, no focal points, and nonpositive curvature.
Abelian subgroups of the fundamental group of a space with no conjugate points, Groups Geom. Dyn. 15 (2021), no. 2, pp. 683-690.
Energy-minimizing maps from manifolds with nonnegative Ricci curvature, Commun. Contemp. Math. 23 (2021), no. 3, 20 pp.
Central splitting of manifolds with no conjugate points, Pacific J. Math. 306 (2020), no. 1, pp. 95-114.
Totally geodesic maps into manifolds with no focal points, Bull. London Math. Soc. 51 (2019), no. 3, pp. 443-458.