ERC Starting Grant · 2017
Categorified Donaldson-Thomas Theory
According to string theory, coherent sheaves on three-dimensional Calabi-Yau spaces encode fundamental properties of the universe. On the other hand, they have a purely mathematical definition. We will develop and use the new field of categorified Donaldson-Thomas (DT) theory, which counts these objects. Via the powerful perspective of noncommutative algebraic geometry, this theory has found application in recent years in a wide variety of contexts, far from classical algebraic geometry. Categorification has proved tremendously powerful across mathematics, for example the entire subject of algebraic topology was started by the categorification of Betti numbers. The categorification of DT…
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