Twistors, black holes and modularity
Résumé
I'll show how twistorial description of quaternionic geometries combined with string theory dualities helped to solve a long standing mathematical problem - to understand modular properties of indefinite theta series. Then I'll use the solution of this problem to describe the modular behavior of the generating
function of degeneracies of BPS black holes appearing in Calabi-Yau compactifications of string theory.