Research Interests

My research has been about physical asymptotics. This concerns physical phenomena that emerge from higher-level, or more general, laws as a parameter becomes large or small. For example, the focal lines and surfaces (caustics) that dominate geometrical optics (and are visible, as bright dancing lines on the bottom of a swimming pool) are not evident in the description of light as electromagnetic waves. Caustics emerge as singularities when the wavelength of the light becomes negligibly small. In quantum mechanics, characteristic correlations between energy levels, associated with classical chaos, emerge semiclassically, that is when Planck's constant is negligible. These limits of physical theories are singular and require the use and development of mathematical tools that include catastrophe theory, divergent series, fractal geometry, and arithmetic zeta functions. Recently, I have been studying the colors of rainbows (short-wave limit) and a popular magnetically levitated top (limit of fast and slow time scales).

Membership Type

International Member

Election Year


Primary Section

Section 13: Physics