John B. Greer, NSF Postdoctoral Research Fellow

John B. Greer Contact Info:

Office Location: 621 Warren Weaver Hall
Office Phone: (212)998-3148
Email Address: greer@cims.nyu.edu

Current Position: I am a National Science Foundation Postdoctoral Research Fellow at the Courant Institute of Mathematical Sciences. Robert V. Kohn is my sponsoring scientist.
Teaching:

Spring 2007:
V63.0140-3 Linear Algebra 11:00-12:50 T Th
Fall 2006:
G63.2701 Applied Mathematics I 7:10-9:00 M
Spring 2006:
V55.0101-2 Math Patterns in Nature 2:00-3:15 T Th
Fall 2005:
V63.0121-5 Calculus I 11:00-12:50 M W
Education:

Ph.D. in Mathematics, Duke Univ., 2003
M.A. in Mathematics, Duke Univ. 2001
B.A., Columbia University 1999
PhD Advisor: Andrea Bertozzi
Research Interests: Nonlinear Partial Differential Equations, Applied Mathematics, Image Processing

Image smoothing and denoising with second and fourth-order diffusion equations. Numerical methods for nonlinear parabolic and hyperbolic PDEs. Computing PDEs in Euclidean space and on curved surfaces. Level set methods. Here is a complete research statement: Research Statement
Curriculum Vitae (Updated October 2006)
Papers

  1. S. Esedoglu and J. B. Greer, Upper bounds on the coarsening rate of discrete, ill-posed nonlinear diffusion equations, Submitted to Comm. Pure Apl. Math. in 2006. [preprint]

  2. J. B. Greer, An improvement of a recent Eulerian method for solving PDEs on general geometries, J. Sci. Comp., vol. 29, no 3, December 2006. [available online] [animations: Allen-Cahn equation on a torus]

  3. J. B. Greer, A. L. Bertozzi, and G. Sapiro, Fourth order partial differential equations on general geometries, J. Comp. Phys., vol. 216 no. 1 (2006), pp. 216-246.[JCP] [animations: Cahn-Hilliard equation and paint dripping down a sphere]

  4. A. L. Bertozzi, J. B. Greer, S. Osher, and K. Vixie, Nonlinear regularizations of TV based PDEs for image processing, AMS Series of Contemporary Mathematics, proceedings of the 2003 Northewestern PDE conference, Gui-Qiang Chen, Joseph Jerome, and George Gasper eds. (2004). [CAM]

  5. A. L. Bertozzi and J. B. Greer, Low curvature image simplifiers: global regularity of smooth solutions and Laplacian limiting schemes, Comm. Pure Appl. Math., vol. 57 no. 6 (2004), pp. 764-790.

  6. J. B. Greer and A. L. Bertozzi, Traveling Wave Solutions of Fourth Order PDEs for Image Processing, SIAM J. Math. Anal., vol. 36 no. 1 (2004), pp. 38-68. [[42737]]

  7. J. B. Greer and A. L. Bertozzi, H^1 Solutions of a Class of Fourth Order Nonlinear Equations for Image Processing, Journal of Discrete and Continuous Dynamical Systems. Special issue in honor of Mark Vishik. Fall 2003.
Dissertation: Fourth order diffusions in image processing.
Me in a kayak

The Independence

When not doing math, I like to kayak.

Whitewater pictures.