### Abstract

Vacuum (Casimir) energy, a topic of great current interest in physics, has close connections with spectral asymptotics, semiclassical approximations, periodic orbits, stationary-phase approximations, quantum graphs, etc. The Casimir effect is observable as the mutual attraction of neutral conducting or dielectric bodies via quantum fluctuations of the electromagnetic field; it is speculated that some related effect is responsible for the observed cosmological "dark energy". I will describe some current progress and issues in this field that are of mathematical interest. For example, contributions to vacuum energy arise from the oscillations in spectral densities associated with periodic classical paths of the associated classical (or ray-optical) system, and the sign of such a contribution is influenced by the phase of the oscillation (the Maslov index or a generalization thereof).

### Related Links

- http://www.math.tamu.edu/~fulling - personal home page
- http://www.math.tamu.edu/~fulling/semivac.html - record of Jan. 2005 workshop