Solving systems of polynomial equations is a classical subject with a long history. It was one of the motivations in the classical development of Algebra and Algebraic Geometry. It was one of the mainpursuits of early Numerical Analysis. Yet, our actual knowledge is not enough to solve but a small part of the systems that arise from many subjects, such as chemistry, physics, or engineering.
This workshop will focus on the mathematical foundations of the subject. In particular, we focus on rigorous algorithms for solving dense or sparse polynomial systems, and related issues in algebra, algebraic or differential geometry, numerical analysis, and applications to algebraic differential equations.