Numerical methods for differential equations evolving on manifolds can be classified as geometric integration techniques, a subject which has undergone significant advances in recent years, in particular under the impetus of Peter Crouch at Arizona State University. A primary goal of the ongoing research is to construct numerical integration methods which preserve important geometric and qualitative features of the analytical solution. These schemes generalize standard approaches and may provide a better understanding of traditional methods.

The purpose of this workshop is, of course, manifold:

• give a tutorial overview of state of the art techniques for solving Ordinary Differential Equations on manifolds, including a theoretical background and illustrated examples from engineering applications;
• spark an interest among Mathematics and engineering graduate students, as well as representatives of local industry, who are encouraged to attend; the topic is also of particular interest to faculty in engineering, physics, chemistry, and more generally any domain where conservation laws play an important role in the numerical treatment of practical problems;
• bring together leading scholars in the field and provide a platform for discussing new ideas and future directions.

The support of

• the Department of Mathematics
• the Center for System Science and Engineering Research
• the College of Engineering
• the College of Liberal Arts and Sciences
• the Office of the Vice-Provost for Research