ABHYANKAR 82nd BIRTHDAY CONFERENCE SPEAKER: Wenhua Zhao (Illinois State) TITLE: Differential Equation and Differential Operator Approaches of the Jacobian Conjecture. ABSTRACT: We first discuss some equivalent formulations of the Jacobian conjecture in terms of the Inviscid Burgers' Equation, the heat equation and the Laplace Operator. We then discuss the Image conjecture, a conjecture on images of differential operators of order one with constant leading coefficients, and its relation with the Jacobian conjecture.