  Understanding vanishing transmission in Fano resonances in quantum systems
and metamaterials, and ultralow transmission in disordered media is key to
elucidating optical interactions. Using analytic theory and numerical
simulations, we discover the topological structure and motion under deformation
of transmission zeros in the complex energy plane. We demonstrate the zeros can
be controlled to create ultranarrow Lorentzian lines in spectra of transmission
time and diverging rates of frequency change of transmission zeros as they
converge. This suggests a new approach to ultrasensitive detection.
