Multidimensional Polylogarithms

Abstract. Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler Sums (or multiple harmonic sums), which, within the past decade, have arisen in knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler Sums, and the Riemann Zeta function. There are a wide variety of interesting results and evaluations for these functions - some conjectured, and some recently proved. This talk will survey the latest results and techniques that have been developed in this area.