Progress on Polynomial Identity Testing

The problem of Identity Testing consists in given an arithmetic circuit that computes a polynomial p in a field, decide whether p is the zero polynomial. One of the first examples of probabilistic algorithms is the polynomial time randomized solution to this problem given by Schwartz and Zippel. More recently there has been considerable progress in trying to find a polynomial time deterministic solution to this important problem at the borderline between complexity theory and algebra. Nitin Saxena, one of the experts in the area, gives in this survey a beautiful overview of several recent results dealing with the complexity of Polynomial Identity Testing.