**Speaker**: Guoce Xin (Brandeis)

**Title**: A new algorithm on PFD and its application to generalized Dedekind
sums

**Abstract**: Recently, I developed a new algorithm on PFD - partial fraction
decomposition of rational functions. This new algorithm is not only fast
but also has theoretical applications.

Given a rational function *R(x)*, the generalized Dedekind sum is the sum of
*R(a)* over all *n*th roots of unity *a* (often with *a = 1*
excluded). Such problems arise in several areas of mathematics, such as
number theory and topology.