Projects for Undergraduate and Graduate Students
Applied mathematics is where one can see "hands-on" how math is useful in virtually any field of the natural sciences. It is fascinating, beautiful, frustrating and rewarding.
To start working together, you should be ok with calculus and analysis, linear algebra and differential equations. Some physics background and familiarity with Maple or Matlab wouldn't hurt, but are not necessary. Overall, imagination and willingness to learn are most appreciated.
For higher level projects we'll use group theory, differential geometry, topology, functional analysis and, to be honest, whatever kind of math is needed for the problem in question.
Below are some research themes I find interesting. However, if you are curious about a particular problem, please come and talk to me.
Roto-vibrational states for molecules
Dynamics of point vortices (Note: point vortices model cyclones and hurricanes)
Stability of Saturn's rings
Dynamics and control of Solar Sails (Note: a Solar Sail is a light space-vessel that uses the Sun radiation pressure for propulsion)
Mathematics of river pollution