What does it mean to solve a polynomial system? Depending whether this problem is seen from a pure computer algebra or from a pure numerical analysis point of view, the answers to this question will be vastly different. In recent years we have seen the development of symbolic-numeric computing. This has led to a more unified view, with challenges common to new fields like "numerical polynomial algebra" and "numerical algebraic geometry".
Graduate Student Colloquium at UIC, 11 March 2005.