The solution of polynomial algebraic equations is common in the design of efficient numerical and optimisation techniques. Examples include highly accurate quadrature methods in numerical analysis and semi-definite programming relaxation in optimisation.The feasibility of solution techniques is often due to the special structure of these problems. For more general problems, direct solvers used for polynomial systems are based on Buchberger's algorithm. These techniques yield exact answers, yet have prohibitively high computational cost even for moderate-sized problems. They are also affected by numerical instabilities and floating point errors.

Topics of the workshop include: computational algebraic geometry and floating point arithmetic, convex algebraic geometry, polynomial systems of equations and optimisation problems, semialgebraic problems (i.e., polynomials systems with polynomial constraints)

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