Modularity of Donaldson-Thomas Invariants on Calabi-Yau Threefolds

Explore a comprehensive lecture on the modularity of Donaldson-Thomas invariants on Calabi-Yau threefolds. Delve into the mathematical representation of BPS indices, which count black hole micro-states in string compactifications. Discover the challenges in computing these invariants and their susceptibility to wall-crossing phenomena. Examine string dualities' prediction of modular or mock modular behavior in generating series of DT invariants counting D4-D2-D0 black holes. Learn about the computation process for one-parameter CY threefolds like the quintic, using vanishing theorems and wall-crossing formulae to find a unique modular completion. Uncover how this approach leads to predictions of new Gopakumar-Vafa invariants and determines topological string amplitudes at higher genera. Based on collaborative work with Sergey Alexandrov, Soheyla Feyzbakhsh, Albrecht Klemm, and Thorsten Schimmanek, this talk by Boris Pioline from LPTHE – Sorbonne Université offers valuable insights into advanced mathematical concepts in string theory and algebraic geometry.