In this thesis we examine the counting of BPS states using wall-crossing, holomorphic anomalies and modularity. We count BPS states that arise in two setups: multiple M5-branes wrapping P x T<sup>2</sup>, where P denotes ...
This thesis presents various corrections to F-theory compactifications which rely on the computation of refined Bogomol'nyi-Prasad-Sommerfield (BPS) invariants and the analysis of backreacted geometries. <br /> Detailed ...