edited by Li Guo (Rutgers University, Newark, USA) & William Y Sit (City College of New York, USA)

Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations.

These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.

• Painlevé Equations
• Hopf Algebra of Trees
• Picard–Vessiot Closure
• Model Theory and Differential Galois Theory
• Frobenius Structures in Differential Algebra
• Computability and Differential Fields
• Jacobi's Bound and Normal Forms Computations
• Linear Differential Equations and Lie Algebras