ISRMT Seminar: The spectral theory of finite Hilbert transforms acting on many intervals.

Roughly 15 years ago, Alexander Katsevich, motivated by tomography, began to study the singular values of the finite Hilbert transform (FHT) acting on interval subsets of the real line. This was the beginning of a (ongoing) program that has produced 10+ papers by 5 authors dedicated to the spectral theory of the FHT. We mention some of the history, the connection to tomography and conclude by discussing our latest result, which deals with the diagonalization of the FHT acting on many intervals with touching endpoints.