Title: A Survey of the Illustrious Jacobian Conjecture

Abstract: The celebrated Jacobian Conjecture asserts:

Let F be a polynomial map from C^n to C^n.  If the jacobian determinant of F is everywhere non-vanishing, then F is a polynomial automorphism.

This conjecture, now 82 years old and still unsolved for n>1, can be viewed as a problem in differential geometry, algebraic geometry, commutative algebra, analysis, topology, and combinatorics.  Over the years it has proved to be remarkably elusive and deceptive, with numerous false proofs appearing, some published by notable  mathematicians.  In this talk we will recount this sometimes amusing story, name the key players, discuss some of the problem’s subtle obstructions, state known reductions of the problem, identify cases where it has been proved to be true, and state equivalent formulations.