Speaker: Boris Pioline (LPTHE, Paris)

Abstract: A central problem in quantum gravity is to get a quantitative
microscopic interpretation of the Bekenstein-Hawking entropy of black
holes. In type II strings compactified on a Calabi-Yau manifold, BPS
black hole microstates are realized by bound states of D-branes
wrapped along complex submanifolds, or in mathematical terms by
"stable coherent sheaves". String dualities predict that suitable
generating series of indices counting such BPS states have modular
properties, although the mathematical origin of modularity is still
mysterious.  I will explain some recent progress in computing these
BPS indices using relations to topological string theory and
wall-crossing, and present strong evidence that modularity is indeed
at work.