Teaching
Courses taught most frequently (click for typical syllabus)
Scientific Computing: Continuous Systems (Math 222)
Partial Differential Equations (Math 397)
Dynamical Systems and Chaos (Math 397)
Calculus "Two and a Half" (Math 115)
Differential Equations (Math 204)
Research
Interests include:
- Equilibrium problems for elastic rods, including incorporating the effect of nontrivial intrinsic shape, and considering a broad range of boundary conditions, especially those relevant to DNA cyclization or looping
- Stability theories in the calculus of variations, generalizing the classic "conjugate point" results to a broader class of problems, including those where the Euler-Lagrange and Jacobi equations are integrodifferential equations (e.g., elastic rods with self-contact)
- Computation of the end-to-end probability density function for an elastic rod and its application to DNA cyclization and looping experiments (collaboration with John Maddocks' group at EPFL); both "exact" (Monte Carlo) and approximate theories, and within rigid-base, rigid-basepair, and continuum models of DNA
- Collaborative projects with biological scientists (has included AFM analysis, aggregation modeling, and epidemiology of viral hemorrhagic fever)