Résumé
Motivated by mathematical structures appearing in gauge and string theories with N=2 supersymmetry, I’ll consider the behavior of certain generalized theta series under Kontsevich-Soibelman transformations. In Calabi-Yau string vacua, such theta series encode instanton corrections from NS5-branes, and their transformation properties ensure the mutual consistency of NS5-instantons, D-instantons and wallcrossing. It turns out that the transformations are captured by Faddeev’s quantum dilogarithm, and lead to a new type of quantum dilogarithm identities with the quantization parameter inversely proportional to the NS5-brane charge.