• Control Theory & Differential Games
• Front Propagation Problems
• Anisotropy & Homogenization
• Pareto & multi-modular optimization
• Elimination Theory
• Computability & Complexity
• Approximate & Probabilistic Algorithms
• Computational Geometry
• Error Analysis

Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes (with J. A. Sethian), Proc. Natl. Acad. Sci. USA 97 no. 11 (2000), 5699–5703.

Ordered upwind methods for static Hamilton-Jacobi equations: theory & algorithms (with J. A. Sethian), SIAM Journal on Numerical Analysis 41 no. 1 (2003), 325–363.

A fast method for approximating invariant manifolds (with J. Guckenheimer), SIAM J. on Applied Dynamical Systems 3 no. 3 (2004) 232–260.

A survey of methods for computing (un)stable manifolds of vector fields (with M. Dellnitz, E. J. Doedel, J. Guckenheimer, M. E. Henderson, O. Junge, B. Krauskopf, and H. M. Osinga), Int. J. Bifurcation and Chaos 15 no. 3 (2005), 763–791.

Static PDEs for time-dependent control problems, Interfaces and Free Boundaries 8 no. 3 (2006), 281–300.

Label-setting methods for multimode stochastic shortest path problems on graphs, Mathematics of Operations Research (to appear).

• Ph.D., Applied Mathematics, University of California, Berkeley (2001).
  
• B.A., Applied Mathematics (with high honors), University of California, Berkeley (1995).