Evaluating Multi-dimensional Polylogarithmic Sums

Abstract. In recent years, there has been a flurry of activity in both the mathematics and physics communities concerning Euler sums. The sums occur within the context of knot theory and quantum field theory, and the field is currently replete with beautiful, yet unproven conjectures. Even more recently, alternating sums have come to the fore, and joint work with J. Borwein and D. Broadhurst has yielded many new results and conjectures for these sums as well. In this talk, I will discuss many of these results, and give an indication of what is known about them.