"Precise Timing in the Auditory Brain Stem" Abstract: A fundamental problem in neurobiology is to understand how the central nervous system performs accurate calculations with components (neurons) whose properties vary across cells and across time and which give variable responses under repeated trials. As one example, we will discuss the sharpening of timing information in auditory brainstem. We will use techniques of probability, analysis, asymptotics and dynamical systems to study the efficacy of coincidence detection as a mechanism to create precise timers.