Date: Tuesday, September 23, 2008
Title: Elliptic curves and Multiple zeta numbers
Abstract: Multiple zeta numbers generalize the values of the Riemann zeta function at
integers larger than 1. They were first considered by Euler and have recently
resurfaced in the works of Zagier, Goncharov and others. The multiple zeta value
$\zeta(n_1,\dots,n_r)$ is defined by
$$
\zeta(n_1,\dots,n_r) =
\sum_{01$. Multiple zeta numbers
occur as periods of the {\em mixed Tate motives}, constructed by Deligne and
Goncharov. They satisfy many interesting combinatorial identities; and some of
their transcendence properties are controlled by the algebraic $K$theory of the
integers.
After surveying these results, I will discuss some mysterious identities between
multiple zeta values that arise from cusp forms for $\SL_2(\Z)$ that go back to
Goncharov and are due to Gangl, Kaneko and Zagier. The final goal is to explain
why the theory of {\em elliptic motives} should explain these mysterious
relations.
Speaker: Richard Hain
Institution: Duke University
