A well known principle in physics asserts that string theory on an orbifold X is equivalent to string theory on Y, any crepant resolution of X. Gromov-Witten theory is the mathematical counterpart of type IIA topological string theory and so it is expected that one can recover the Gromov-Witten invariants of Y from those on X. We will mathematically formulate and discuss this correspondence and illustrate it with some examples. Time permitting, we will also discuss a version of the correspondence for Donaldson-Thomas theory.

Lecture #12364

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