Modularity of Donaldson-Thomas Invariants on Compact Calabi-Yau Threefolds

Explore the mathematical intricacies of Donaldson-Thomas invariants in this comprehensive lecture on compact Calabi-Yau threefolds. Delve into the challenges of computing these invariants, which represent BPS indices counting black hole micro-states in string compactifications, and examine their wall-crossing phenomena. Discover how string dualities predict modular or mock modular behavior in generating series of DT invariants for D4-D2-D0 black holes. Learn about the computation methods for one-parameter CY threefolds like the quintic, using vanishing theorems and wall-crossing formulae to find unique modular completions. Understand how these findings lead to predictions of new Gopakumar-Vafa invariants and advancements in determining topological string amplitudes. If time allows, explore modularity in two-parameter CY threefolds with elliptic or K3 fibrations. This lecture is based on collaborative work with Sergey Alexandrov, Soheyla Feyzbakhsh, Albrecht Klemm, Thorsten Schimmanek, and upcoming research with Charles Doran.