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.

Boris Pioline: Modularity of Donaldon-Thomas invariants on compact Calabi-Yau threefolds #ICBS2024