CECM Colloquium

**Wednesday January 30,
in K9509, SFU
**

3:30 - 4:20

Dr Hoang Ngoc Minh

University of Lille 2 - CNRS (France)
on leave at MIT (USA).

**Title:**
"The algorithmic and combinatoric aspects of functional
equations for polylogarithms."

**Abstract:**
The algebra of polylogarithms is the smallest $\bf C$-algebra which
contains the constants and which is stable under integration with
respect to the differential forms $dz/z$ and $dz/(1-z)$. It is known
that this algebra is isomorphic to the algebra of the noncommutative
polynomials equipped with the shuffle product. As a consequence, the
polylogarithms $Li_n(g(z))$ with $n\ge1$, where the $g(z)$ belong to
the group of biratios, are polynomial on the polylogarithms indexed by
Lyndon words with coefficients in a certain transcendental extension of
$\bf Q$~: $\bf MZV$, the algebra of the Euler-Zagier sums. The
question of knowing whether the polylogarithms $Li_n(g(z))$ satisfy a
linear functional equation is effectively decidable up to a
construction of a basis for the algebra $\bf MZV$.