Donaldson-Thomas Invariants

Donaldson–Thomas invariants are advanced mathematical tools used in algebraic geometry to count certain geometric objects called stable sheaves or subvarieties on Calabi–Yau threefolds. They serve as sophisticated "counts" of these objects, capturing their complex structures and symmetries in a way that remains meaningful even when straightforward counting is impossible. These invariants help mathematicians understand the geometry and topology of complex spaces relevant to string theory and theoretical physics, providing deep insights into the structure of the universe at a fundamental level.