This proposal concerns enumerative invariants. These record the number of curves in a space X that have specified properties. They carry a great deal of subtle information about the geometry of X, and they are also important in string theory, where the curves represent worldsheets of strings propagating in the spacetime X.
The connection with string theory sheds great light on the structures formed by curve-counting invariants, and suggests that the different types of enumerative counting invariants
are closely related. In this project, we will develop new tools to compare enumerative invariants and new methods to calculate them.
Call for proposal
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