The Algebra, Analysis and Combinatorics of Multidimensional Polylogarithms

Abstract. Multidimensional polylogarithms represent a nested sum extension of the classical polylogarithm and the Riemann Zeta function. Not surprisingly, there are a wide variety of interesting results and evaluations for these functions---some conjectured, and some recently proved. This talk will survey some of the highlights, and describe techniques from algebra, analysis and combinatorics which have been developed to study these functions.