Research Interests

My area of research is differential geometry. My dissertation work contained some results on Ricci flow and other results on general relativity. More recently, I have helped a physics colleague analyze a specific model for crystal growth and worked on a Hall effect problem with another group of colleagues in physics.

During the summer of 2002, I advised Jason Preszler, an undergraduate here at the University of Puget Sound, on his summer research project. Jason studied the curve shortening problem for knots and analyzed how writhe evolves under the curve shortening flow. His report on his progress and results is available here as a PDF file.

Recent talks

"Using Ricci flow to improve the shape of your manifold (and to prove the Poincare Conjecture)", Pacific Lutheran University Undergraduate Math Seminar, April 4, 2007

Density in the calculus sequence PNW MAA April 10, 2010

"Using symmetry to solve differential equations", Lewis & Clark College Mathematics Colloquium, March 6, 2012

Research publications

J. Isenberg, M. Jackson, and P. Lu, "Ricci Flow on Locally Homogeneous Closed 4-Manifolds", Communications in Analysis and Geometry, 14, 345-386, 2006.

M.J. Moelter, J. Evans, G. Elliot, and M. Jackson, ``Electric potential in the classical Hall effect: An unusual boundary-value problem,'' American Journal of Physics, 66, 668-676, 1998

J.S. Wettlaufer, M. Jackson, and M. Elbaum, ``A geometric model for anisotropic crystal growth,'' Journal of Physics A, 27, 5957-5968, 1994.

J. Isenberg and M. Jackson, ``Ricci flow on minisuperspaces and the geometry-topology problem,'' in Directions in General Relativity, Volume 1, B.L. Hu and T.A. Jacobson (Eds.), Cambridge University Press, 1993.

J. Isenberg and M. Jackson, ``Ricci flow of locally homogeneous geometries on closed manifolds,'' Journal of Differential Geometry, 35, 723-741, 1992.

J. Isenberg, M. Jackson, and V. Moncrief, ``Evolution of the Bel-Robinson energy in Gowdy T3×IR spacetimes,'' Journal of Mathematical Physics, 31, 517-519, 1990.

M. Carfora, J. Isenberg, and M. Jackson, ``Convergence of the Ricci flow for a class of Riemannian metrics with indefinite Ricci curvature,'' Journal of Differential Geometry, 31, 249-263, 1990.