This workshop will focus on how mathematics can help us determine the functional roles that oscillations play in the nervous system. This workshop is timely in view of recent evidence that oscillations are critical for cognitive states and sensory processing. A broad range of oscillatory activity will be covered, including hippocampal and cortical oscillations, motor patterns, sensory processing and circadian rhythms. Competing theories will be presented on controversial issues, such as the role of gamma oscillations in binding of sensory information and the role of theta oscillations in hippocampal circuitry, with a view to how mathematics might help to resolve these controversies. We will try to draw parallels across different systems to see if central organizing principles emerge.
Recent theoretical advances in the understanding of several central pattern generators (CPGs) will be compared and contrasted, including the CPG for coordinating crawfish swimmerets, the CPG for respiratory pattern generation, the pyloric circuit, and spinal CPGs involved in human gaits. Circadian rhythms will be addressed at the level of the molecular clocks underlying the diurnal rhythm and at the level of the interaction of these clocks with the electrical activity of the suprachiasmatic nucleus. Sensory systems will be represented by theoretical and experimental studies on the role of oscillations in distinguishing odors. Theoretical results on the nonlinear dynamics of coupled oscillators in the presence of noise will be presented and integrated into the context of the specific examples presented for different systems.