Significant applications of mathematics to biology have occurred for nearly a century, starting from the early work of Vito Volterra and Alfred Lotka on interacting populations, and maturing through fundamental work in population genetics (Haldane, Fisher, and Wright), epidemiology (Ross, Kermach and MacKendrick), development (Turing) and neurobiology (Hodgkin and Huxley, Fitzhugh and Nagumo, McCulloch and Pitts). Much of this research stimulated important contributions by other mathematicians (Kolmogorov, Petrovsky, Piscunox, Karlin, etc.); in general, however, until the past 10--20 years, communication between mathematicians and biologists remained problematical; much work in mathematical biology was relatively sterile, unsullied by contact with data, while experimental work suffered from a lack of theoretical generality.
The situation has changed dramatically in the past decade or so. Today's biologists are, in many areas, very sophisticated mathematically; mathematicians have learned the importance of becoming immersed in data; and the spectrum of practitioners has filled in, providing a continuum of highly mathematical work to collaborations. New and exciting areas (e.g. molecular biology, epidemiology and immunology) have opened up to mathematical investigations. A century of research has elucidated fundamental mechanisms in evolution, collective phenomena and pattern formation, and laid the foundations for more specialized modeling; and the development of new computational tools has greatly expanded the potential both for fundamental studies and for communications.
Thus the time is right for this special year at the IMA, built upon a selected series of workshops highlighting some of the mathematical challenges emerging from the consideration of biological issues, and endeavoring to show how the mathematics can be applied to the resolution of those issues. This program focuses on some particularly rich areas of investigation, complementing activities which have been carried out at the IMA in MRI, molecular biology and neurobiology in earlier years.