Georgia Institute of Technology College of Sciences

The polynomials mentioned in the title were introduced by Cauchy and Liouville in 1839 in connection with early attempts at a proof of Fermat's Last Theorem. They were subsequently studied by Mirimanoff who in 1903 conjectured their irreducibility over the rationals. During the past fifteen years it has become clear that Mirimanoff's conjecture is closely related to properties of certain special functions and to some deep results in diophantine approximation. Apparently, there is also a striking connection to hierarchies of certain evolution equations (which this speaker is not qualified to address). We will present and discuss a number of recent results on this problem.