It has been known for some time that the solution profile of dispersive equations posed on periodic domains depends heavily on the algebraic properties of time, a phenomenon called Talbot effect in the literature. In this project we will set up numerical experiments to study this behavior for model linear equations such as the Schrodinger equation posed on the two-dimensional sphere. Specifically, we will numerically test the optimality of the limited results known for the fractal dimension of the graphs of solutions to certain linear equations.
Experience with python is a must. Some experience with differential equations would be useful but it is not crucial.