Mathematical Sciences: Symmetries and Integrability of Difference Equations

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9402625 Miller This award covers partial expenses for U.S. research mathematicians to participate in a workshop whose primary focus concerns symmetries and integrability of difference equations. The motivation lies in efforts to develop tools for solving nonlinear differential equations. There are two main methods, one involves Lie group theory, the other is integrability theory. A notable development in the last twenty years exemplifying integrability theory was the introduction of the inverse scattering transform. A much more recent development is that similar techniques are being successfully applied to solve equations that involve discrete variables: difference and differential-difference equations. Such equations are important in physics in their own right, in the study of discrete systems and theories on lattices, cellular automata, etc. Moreover, difference equations an variations thereof have gained great prominence recently in the theory and applications of quantum groups. The workshop brings together contingents of leading researchers from the United States and Canada together with a sizable number of graduate students and postdoctoral faculty to work together, with few formal lectures, for a period of seven days on issues related to some of the truly exciting emerging areas of mathematics and mathematical physics. ***