Millions of people suffer from some form of neurological disease, and abnormalities in brain circuits and their activities are recognized as a place to focus in untangling brain disorders. Oscillations and dynamic behaviour produced by neuronal circuits are being examined in the context of several neurological diseases today. While the functional aspect of the observed dynamics is not entirely clear, it is clear that cellular aspects of circuits need to be included in these examinations as specific cell types have been associated with network dysfunction and neurological disease. A mechanistic understanding, as can be brought about by mathematical modeling and analyses, is needed to help advance our understanding of these complex neurological diseases. However, developing and analyzing models of normal and pathological dynamic activities in these complex circuits is highly challenging. This is not only because of the complexity and detail of the systems themselves, but also because of the required multi-disciplinary aspect of the work. How does one include cellular detail in mathematical models to allow linkage to experiment and neurological disease? What techniques and methods can and should be used to analyze the models? These difficult questions need to be brought to the fore to allow us to move forth in our understanding and to provide insights that would be helpful from diagnostic and drug development perspectives.

In a series of workshops we will bring together neuroscientists, mathematicians, clinicians and experimentalists to present and consider these problems from several viewpoints. Speakers in the workshops (as listed below) will present from clinical, experimental, modeling, and mathematical perspectives. Mathematical tutorial type talks will occur over the course of the workshops covering topics such as phase plane analyses, weakly coupled oscillator theory, perturbation theory, bifurcation theory, mean field analyses, and numerical tools. Each workshop will end with a "brainstorming session" for discussion, interaction and sharing of perspectives by all to try to propose, define, and/or formulate mathematical and computational problems relevant to the focus, and to identify where further models and mathematical analyses are most warranted. The workshops will be preceded by basic tutorial sessions, and additional discussion and research time will be available after the workshops

Goals for this program include: (i) encouraging trainees in mathematics, physical sciences, life sciences, and interdisciplinary studies, especially new researchers and mathematicians, to get involved in this exciting and challenging field of research, (ii) making neuroscientists more aware of the mathematical tools available to aid with the study of network models, (iii) making mathematicians more aware of the challenges involved in modeling biological networks, and (iv) initiating collaborations.