A set of polynomials is said to be algebraically independent if there is no non-zero combination of them which is zero. Testing whether a given set of polynomials is algebraically independent efficiently is open in general. However, when the underlying field has characteristic zero, the Jacobian criterion reduces algebraic independence testing to linear independence testing. This leads to a randomized poly-time algorithm in this case.
In this talk, we will look at the Jacobian Criterion and if time permits, see its connection to the Polynomial Identity Testing question in Algebraic Circuits.