Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Masha Vlasenko
Affiliation:

MPIM
Date:

Wed, 02/06/2010 - 15:00 - 16:00 We consider certain $r$-fold $q$-hypergeometric series depending on several rational parameters. These series arise in conformal field theory and it is of interest to know for which values of parameters they are modular. A conjectural (partial) answer by Werner Nahm surprisingly involves dilogarithms and the Bloch group. This conjecture was proved by Don Zagier for rank $r=1$ and also tested numerically by him and Michael Terhoeven for higher ranks $r>1$. We develop a general method of finding values of parameters corresponding to modular cases and apply it for $r=1$ (reproving Zagier's result) and $r=2$ (obtaining several modular cases not known earlier).

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/246