The "Math" part of our interview with Dr. Linowitz, a number theorist and differential geometer at Oberlin College. Dr. Linowitz grew up (mathematically, that is) in algebraic number theory. These days he works in inverse spectral geometry. We talk about how this field developed from a single, famous theoretical math problem, the "can you hear the shape of a drum problem". We learn that the "hearing" part of the problem refers to the spectrum (i.e. the eigenvalues) of a particular differential operator, the Laplace operator.

Because the Laplace operator exists on many Riemannian manifolds, this famous problem can be generalized to that setting. Dr. Linowitz specializes in special classes of manifolds which are negatively curved, hyperbolic manifolds.

We hear how algebraic number theory enters the picture, as many of these hyperbolic manifolds can be created using techniques from number theory. Dr. Linowitz shares an excellent example of how expertise in one field (here it's algebraic number theory) can be used to prove results in another (inverse spectral geometry).

Dr. Linowitz's gave a great interview and has a gift for explaining things lucidly. I highly recommend hearing what he has to say.