Interference, Caustics and Oscillatory Integrals

Interference is one of the most universal phenomena in nature. In classical physics, the linear superposition of sound waves, surface waves, radio waves, light or gravitational waves all exhibit the same characteristic patterns of constructive and destructive interference. Interference is also fundamental to quantum physics, as exemplified by the Feynman path integral. However, interference patterns are often surprisingly hard to compute. In particular in the vicinity of caustics, where the waves interfere constructively.

The study of interference phenomena often requires the evaluation of a highly oscillatory (multi-dimensional) integral whose convergence is delicate. In this talk, I discuss a new technique known as Picard-Lefschetz theory. This application of Cauchy's integral theorem, from complex analysis, provides an unambiguous definition of these integrals and enables us to analytically approximate and numerically evaluate them. I will demonstrate this method in radio astronomy and in simple models of the quantum big bang, and describe ongoing efforts to apply the framework to the Feynman path integral and quantum gravity.

This event will be available to attend in-person and online. Note, the room has limited space available, so we will work on a first come, first served principle.

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