Abstract: There are many situations in mathematics and its applications where the zeros of a distribution (or of its transform) are critical to understanding the structure of the distribution. This lecture will focus on two examples of this phenomenon. One example is the phase retrieval problem: finding a discrete or continuous distribution knowing only the intensity of its Fourier transform. Here the zeros of the transform are the key to factorization methods that characterize the non-uniqueness in the phase retrieval problem. Algorithms for retrieving a distribution from the zeros of its transform lead to interesting issues of approximation and extrapolation. Another example of zeros determining structure is in the inverse problem of determining an electrostatic field from its measured values. How much data is needed to determine the field becomes the challenge of understanding the structure of the zero set of
the field.

Refreshments at 4:30 in 657 Rhodes Hall.