Todd Drumm, Ph.D.
Department of Mathematics
Washington DC 20059
Room 214 ASB
Ph.D. (1990) University of Maryland
Research Interests: Lorentzian Geometry, Hyperbolic Geometry, 3-D Polyhedra
Much of my research has been concerned with Lorentzian geometry, the natural home of Einstein's theory of special relativity and where you can walk a crooked mile to find a crooked plane and a crooked half-space. I am particularly interested in the applications of Lorentzian geometry to its close relative, hyperbolic geometry.
I am also interested in understanding the geometry of the bidisk, the hyperbolic plane cross the hyperbolic plane, more fully.
One of my visualization projects is to draw polygonal flat tori, and other translation surfaces in 3-space.
- A Primer on the (2+1) Einstein Universe, to appear in Recent developments in pseudo-Riemannian Geometry, ESI-Series on Mathematics and Physics (with T. Barbot, V. Charette, W. Goldman and K. Melnick)
- Strong isospectrality of Lorentz space-times,J. Diff. Geom. 66 (2004), pp. 451 - 466 (with V. Charette)
- Closed timelike curves in flat Lorentz spacetimes,J. Geom. and Phys. 46, Issues 3 - 4 (2003), pp. 394 - 408 (with V. Charette, and D. Brill)
- Ford and Dirichlet domains for cyclic subgroups of PSL(2,C) acting on H^3 and dH^3, Conform. Geom. Dynam. 3 (1999), pp. 116 - 150 (with J. Poritz)
- The geometry of crooked plane, Topology 38, No. 2 (1999), pp. 323 - 352 (with W. Goldman)
- Linear holonomy of Margulis space-times, J. Diff. Geom. 38, No. 3 (1993), pp. 679 - 691
- Fundamental polyhedra for Margulis space-times, Topology, 31, No. 4 (1992), pp. 677 - 683