Donaldson-Thomas theory

Donaldson-Thomas theory is a branch of mathematics that counts certain geometric structures called "sheaves" on complex three-dimensional shapes known as Calabi-Yau threefolds. These sheaves can be thought of as ways to organize how fields or objects distribute over the space. The theory provides algebraic invariants—numbers or functions—that encapsulate key geometric and physical properties of these spaces, connecting deep areas in geometry, string theory, and mathematical physics. Essentially, it offers a rigorous way to count and analyze complex features of these intricate spaces, enriching our understanding of their structure and symmetries.