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Explore the modular properties of generating functions for rank 0 Donaldson-Thomas invariants in this 1-hour 5-minute conference talk. Delve into the physical origin of these properties and their connection to D4-D2-D0 BPS indices in Calabi-Yau compactifications of string theory. Learn how these properties can be utilized to determine generating functions up to a finite number of coefficients, known as polar terms, which can be fixed through wall-crossing. Examine the implementation of this program for compact one-parameter Calabi-Yau threefolds with 2 units of D4-brane charge, resulting in explicit mock modular forms that encode BPS indices. Discover a general solution to modular anomaly equations using indefinite theta series for higher charges, where polar terms remain challenging to access.
