Donalsson-Thomas Invariants

Donalsson-Thomas invariants are mathematical tools used in algebraic geometry and string theory to count certain geometric structures—specifically, stable objects like sheaves or curves—on complex shapes called Calabi–Yau manifolds. They provide a way to quantify these objects in a way that remains consistent under continuous transformations of the space, making them “invariants.” These counts help mathematicians and physicists understand the intricate geometry of these spaces and have applications in understanding fundamental physics, such as string theory. Essentially, Donalsson-Thomas invariants are sophisticated counting methods that reveal deep geometric and physical insights.