This workshop is devoted to algorithmic developments in Combinatorics and Differential Algebra with a particular focus on the interaction of these two areas.

Symbolic Combinatorics: Symbolic algorithms and software have recently been developed that allow researchers to discover and prove combinatorial identities as well as understand analytic and algebraic properties of generating functions. These functions seldom have closed form solutions and even when they do, direct evaluation may be intractable. Recent work in Symbolic Combinatorics has focused on representing such functions by annihilating differential or difference operators and then using techniques from differential and difference algebra, as well as analysis, to analyze these equations and their solutions. Besides methods relating to creative telescoping and verication of function identities, other areas of emphasis will include effective methods in difference algebra, the Galois theories of difference equations, and the interaction of differential and difference algebra in combinatorics.

Computational Differential Algebra is an approach to nonlinear or linear differential equations and differential structures, focusing not only on finding explicit closed form solution, but also on simplifying such equations to yield preconditioning for subsequent numerical solution, as well clearer understanding of the qualitative behavior of solutions. Highlighted aspects will include differential-elimination completion algorithms; geometric differential algebra, moving frames and differential invariants; differential Galois theory and integrability; complexity and open problems.